Loop-and-allied QG bibliography

[atyy]

http://arxiv.org/abs/1606.04044
Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
Joseph Ben Geloun, Tim A. Koslowski
(Submitted on 13 Jun 2016)
We investigate the universality classes of rank-4 colored bipartite U(1) tensor field models near the Gaussian fixed point with the functional renormalization group. In a truncation that contains all power counting relevant and marginal operators, we find a one-dimensional UV attractor that is connected with the Gaussian fixed point. Hence this is first evidence that the model could be asymptotically safe due to a mechanism similar to the one found in the Grosse-Wulkenhaar model, whose UV behavior near the Gaussian fixed point is also described by one-dimensional attractor that contains the Gaussian fixed point. However, the cancellation mechanism that is responsible for the simultaneous vanishing of the beta functions is new to tensor models, i.e. it does not occur in vector or matrix models.

 

[atyy]

http://arxiv.org/abs/1606.04932
Geodesic completeness and the lack of strong singularities in loop quantum Kantowski-Sachs spacetime
Sahil Saini, Parampreet Singh
(Submitted on 15 Jun 2016)
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events occur can only for very exotic equations of states when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.

 

[atyy]

http://arxiv.org/abs/1606.07924
Inflationary spectra from near Ω-deformed space-time transition point in Loop Quantum Cosmology
Long Chen, Jian-Yang Zhu
(Submitted on 25 Jun 2016)
Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal a Ω -deformed space-time structure, Ω:=1−2ρ/ρc, where Ω<0 means an Euclidean-like space and Ω>0 means a Lorentz-like space. It would be reasonable to give the initial value at the space-time transition point, ρ=ρc/2, but we find it is impossible to define a Minkowski-like vacuum even for large k-modes at that time. However if we loose the condition and give the initial value near after Ω=0, e.g. Ω≃0.2, the vacuum state can be well defined and furthermore the slow roll approximation also works well in that region. Both scalar and tensor spectra are considered in the framework of loop quantum cosmology with holonomy corrections. We find that if the energy density is not too small compared with ρc/2 when the considered k-mode crossing the horizon, effective theory can give a much smaller scalar power spectrum than classical theory and the spectrum of tensor perturbations could blue shift. But when compared with the observations, since the energy densities when the modes crossed the horizon were quite smaller than ρc, the results we get are the same with previous work in the literature and the classical inflation theory.

 

[atyy]

http://arxiv.org/abs/1607.00910
Big-Bounce cosmology in the presence of Immirzi field
Flavio Bombacigno, Francesco Cianfrani, Giovanni Montani
(Submitted on 4 Jul 2016)
The Immirzi parameter is promoted to be a scalar field and the Hamiltonian analysis of the corresponding dynamical system is performed in the presence of gravity. We identified some SU(2) connections, generalizing Ashtekar-Barbero variables, and we rewrite the constraints in terms of them, setting the classical formulation suitable for loop quantization. Then, we consider the reduced system obtained when restricting to a flat isotropic cosmological model. By mimicking loop quantization via an effective semiclassical treatment, we outline how quantum effects are able to tame the initial singularity both in synchronous time and when the Immirzi field is taken as a relational time.

http://arxiv.org/abs/1607.00955
Thermal Time and Kepler's Second Law
Deepak Vaid
(Submitted on 4 Jul 2016)
It is shown that a recent result regarding the average rate of evolution of a dynamical system at equilibrium in combination with the quantization of geometric areas coming from LQG, implies the validity of Kepler's Second Law of planetary motion.

 

[atyy]

http://arxiv.org/abs/1607.02460
Relationalism Evolves the Universe Through the Big Bang
Tim A Koslowski, Flavio Mercati, David Sloan
(Submitted on 8 Jul 2016)
We investigate the singularities of homogeneous cosmologies from the point of view of relational (and physically relevant) degrees of freedom of the gravitational field. These do not depend on absolute units of length and duration - thus they do not include the volume and extrinsic curvature. We find that the fully relational dynamical system remains well posed for all physical times, even at the point that would be described as the big bang when evolving present day data backwards in time.This result is achieved in two steps: (1) for solutions which are gravity-dominated near the singularity, we show that any extended physical clock (whose readings only depend on the relational degrees of freedom) will undergo an infinite number of ticks before reaching the big bang. The singularity is therefore pushed into the infinite physical past of any physical clock. (2) for solutions where a stiff matter component (e.g. a massless scalar field) dominates at the singularity, we show that the relational degrees of freedom reach the point that is described as the big bang in the dimensionful description of General Relativity (GR) at a finite physical time and evolve smoothly through it, because they are decoupled from the unphysical dimensional degrees of freedom, which are the only ones that turn singular. Describing the relational dynamics with the dimensionful language of GR makes the relational dynamics appear as two singular GR solutions connected at the hypersurface of the singularity in such a way that the relational degrees of freedom evolve continuously while the orientation of the spatial frame is inverted. Our analysis applies to all GR solutions which conform to the BKL conjecture, and is therefore relevant for a large class of cosmological models with inhomogeneity.

 

[atyy]

http://arxiv.org/abs/1605.05268
Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
Marios Christodoulou, Carlo Rovelli, Simone Speziale, Ilya Vilensky
(Submitted on 17 May 2016)
A gravitationally collapsed object can bounce-out from its horizon via a tunnelling process that violates the classical equations in a finite region. Since tunnelling is a non-perturbative phenomenon, it cannot be described in terms of quantum fluctuations around a classical solution and a background-free formulation of quantum gravity is needed to analyze it. Here we use Loop Quantum Gravity to compute the amplitude for this process, in a first approximation. The amplitude determines the tunnelling time as a function of the mass. This is the key information to evaluate the astrophysical relevance of this process. The calculation offers a template and a concrete example of how a background-free quantum theory of gravity can be used to compute a realistical observable quantity.

http://arxiv.org/abs/1606.04444
Statistical mechanics of covariant systems with multi-fingered time
Goffredo Chirco, Thibaut Josset
(Submitted on 14 Jun 2016)
Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.

http://arxiv.org/abs/1607.00364
Quantum Gravity Effects around Sagittarius A*
Hal M. Haggard, Carlo Rovelli
(Submitted on 1 Jul 2016 (v1), last revised 5 Jul 2016 (this version, v2))
Recent VLBI observations have resolved Sagittarius A* at horizon scales. The Event Horizon Telescope is expected to provide increasingly good images of the region around the Schwarzschild radius rS of Sgr A* soon. A number of authors have recently pointed out the possibility that non-perturbative quantum gravitational phenomena could affect the space surrounding a black hole. Here we point out that the existence of a region around 76rS where these effects should be maximal.

http://arxiv.org/abs/1607.04121
Universe's memory and spontaneous coherence in loop quantum cosmology
Tomasz Pawłowski
(Submitted on 14 Jul 2016)
The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology. This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large Universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.

Thanks to @fuzzyfelt for the first 3 suggestions! To everyone: If I've missed any good stuff, please add it directly here on marcus's bibliography on loop quantum gravity and other non-string QG approaches - of course, if strings and LQG converge that would be great too, at least for Smoliners, not sure about Rovellians ;) As I understand, marcus welcomed everyone to contribute. The main rule to observe is that this thread should a bibliography, so if there is a paper we would like to discuss, a new thread dedicated to it should be started (in addition to adding to this bibliopgraphy).

 

[atyy]

http://arxiv.org/abs/1607.05129
An elementary introduction to loop quantum gravity
Norbert Bodendorfer
(Submitted on 18 Jul 2016)
An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and requires only little prior knowledge of quantum mechanics, gauge theory, and general relativity. The main aim of these lectures is to provide non-experts with an elementary understanding of loop quantum gravity and to evaluate the state of the art of the field. Technical details are avoided wherever possible.

 

[atyy]

http://arxiv.org/abs/1607.06227
State refinements and coarse graining in a full theory embedding of loop quantum cosmology
Norbert Bodendorfer
(Submitted on 21 Jul 2016)
Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few "coarse" quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined while the dynamics of the coarse observables is unchanged. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-interacting FRW patches. The technical means to arrive at this result are a version of loop quantum gravity based on variables inspired by loop quantum cosmology, as well as an exact solution to the quantum dynamics of loop quantum cosmology which extends to the full theory in the chosen approximation.

http://arxiv.org/abs/1607.06329
Universal features of quantum bounce in loop quantum cosmology
Tao Zhu, Anzhong Wang, Klaus Kirsten, Gerald Cleaver, Qin Sheng
(Submitted on 20 Jul 2016)
Loop quantum cosmology (LQC) provides an elegant resolution of the classical big bang singularity by a quantum bounce in the deep Planck era. The evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background and its linear scalar and tensor perturbations are universal during the pre-inflationary phase. In this period the potentials of the perturbations can be well approximated by a P\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary models with a single scalar field. Matching them to those given in the slow-roll inflationary phase, we investigate the effects of the quantum bounce on the power spectra and find unique features that can be tested by current and forthcoming observations. In particular, fitting the power spectra to the Planck 2015 data, we find that the universe must have expanded at least 132 e-folds from the bounce until now.

 

[atyy]

http://arxiv.org/abs/1607.05866v1
A note on the architecture of spacetime geometry
Fen Zuo
(Submitted on 20 Jul 2016)
Recently the SU(2) spin-network states in loop quantum gravity is generalized to those of the corresponding Kac-Moody algebra. We show that if one literally starts from the full SL(2,C) group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region. This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers. Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made.
[PLAIN]http://arxiv.org/abs/1607.06662[/PLAIN]
http://arxiv.org/abs/1607.06662
Impact of nonlinear effective interactions on GFT quantum gravity condensates
Andreas G. A. Pithis, Mairi Sakellariadou, Petar Tomov
(Submitted on 21 Jul 2016)
We present the numerical analysis of effectively interacting Group Field Theory (GFT) models in the context of the GFT quantum gravity condensate analogue of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus we go beyond the usually considered construction for free models.
More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behaviour suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated.
Furthermore, we study the expectation values of certain geometric operators imported from Loop Quantum Gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

 

[atyy]

http://arxiv.org/abs/1607.07312
Conformal Anomalies and Gravitational Waves
Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 25 Jul 2016)
We argue that the presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions, whose non-localities can overwhelm the smallness of the Planck scale. The fact that no such effects have been seen in recent cosmological or gravitational wave observations therefore imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. We then show that, among presently known theories, a complete cancellation of conformal anomalies in D=4 for both the C2 invariant and the Euler (Gauss-Bonnet) invariant E4 can only be achieved for N-extended supergravities with N≥5, as well as for M theory compactified to four dimensions.

http://arxiv.org/abs/1607.06888
Holographic bound in covariant loop quantum gravity
Takashi Tamaki
(Submitted on 23 Jul 2016)
We investigate puncture statistics based on the covariant area spectrum in loop quantum gravity. First, we consider Maxwell-Boltzmann statistics with a Gibbs factor for punctures. We establish formulae which relate physical quantities such as horizon area to the parameter characterizing holographic degrees of freedom. We also perform numerical calculations and obtain consistency with these formulae. These results tell us that the holographic bound is satisfied in the large area limit and correction term of the entropy-area law can be proportional to the logarithm of the horizon area. Second, we also consider Bose-Einstein statistics and show that the above formulae are also useful in this case. By applying the formulae, we can understand intrinsic features of Bose-Einstein condensate which corresponds to the case when the horizon area almost consists of punctures in the ground state. When this phenomena occurs, the area is approximately constant against the parameter characterizing the temperature. When this phenomena is broken, the area shows rapid increase which suggests the phase transition from quantum to classical area.

 

[atyy]

http://arxiv.org/abs/1607.07963
Degrees of freedom in discrete geometry
Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen
(Submitted on 27 Jul 2016)
Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices using vectorial (differential form) and coordinate-free pictures, and a consistent procedure to couple particles of space, together with a method to calculate the degrees of freedom of the system of 'quanta' of space in the classical framework.

 

[atyy]

http://arxiv.org/abs/1607.08359
The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
Christoph Charles, Etera R. Livine
(Submitted on 28 Jul 2016)
The closure constraint is a central piece of the mathematics of loop quantum gravity. It encodes the gauge invariance of the spin network states of quantum geometry and provides them with a geometrical interpretation: each decorated vertex of a spin network is dual to a quantized polyhedron in R3. For instance, a 4-valent vertex is interpreted as a tetrahedron determined by the four normal vectors of its faces. We develop a framework where the closure constraint is re-interpreted as a Bianchi identity, with the normals defined as holonomies around the polyhedron faces of a connection (constructed from the spinning geometry interpretation of twisted geometries). This allows us to define closure constraints for hyperbolic tetrahedra (living in the 3-hyperboloid of unit future-oriented spacelike vectors in R3,1) in terms of normals living all in SU(2) or in SB(2,C). The latter fits perfectly with the classical phase space developed for q-deformed loop quantum gravity supposed to account for a non-vanishing cosmological constant Λ>0. This is the first step towards interpreting q-deformed twisted geometries as actual discrete hyperbolic triangulations.

 

[atyy]

http://arxiv.org/abs/1607.08881
Fusion basis for lattice gauge theory and loop quantum gravity
Clement Delcamp, Bianca Dittrich, Aldo Riello
(Submitted on 29 Jul 2016)
We introduce a new basis for the gauge--invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin--network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi--local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse--graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin--network basis, in which it is much more complicated to account for electric excitations, i.e. for Gau\ss~constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi--scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow--up work, we will exploit this notion to provide a new definition of entanglement entropy for these theories.

http://arxiv.org/abs/1607.08629
Statistical discrete geometry
Seramika Ariwahjoedi, Valerio Astuti, Jusak Sali Kosasih, Carlo Rovelli, Freddy Permana Zen
(Submitted on 28 Jul 2016)
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.

 

[atyy]

Holographic relations in loop quantum gravity
Lee Smolin
(Submitted on 9 Aug 2016)
It is shown that a relation between entropy and minimal area holds in loop quantum gravity, reminiscent of the Ryu-Takayanagi relation.

The multitrace matrix model: An alternative to Connes NCG and IKKT model
Badis Ydri
(Submitted on 9 Aug 2016)
We present a new multitrace matrix model, which is a generalization of the real quartic one matrix model, exhibiting dynamical emergence of a fuzzy two-sphere and its non-commutative gauge theory. This provides a novel and a much simpler alternative to Connes non-commutative geometry and to the IKKT matrix model for emergent geometry in two dimensions.

 

[atyy]

http://arxiv.org/abs/1608.04145
Decoherent Histories Quantum Mechanics Starting with Records of What Happens
James B. Hartle
(Submitted on 14 Aug 2016)
We present a formulation of the decoherent (or consistent) histories quantum theory of closed systems starting with records of what histories happen. Alternative routes to a formulation of quantum theory like this one can be useful both for understanding quantum mechanics and for generalizing and extending it to new realms of application and experimental test.

 

[atyy]

http://arxiv.org/abs/1608.04228
Quantum Gravity in the Sky: Interplay between fundamental theory and observations
Abhay Ashtekar, Brajesh Gupt
(Submitted on 15 Aug 2016)
Observational missions have provided us with a reliable model of the evolution of the universe starting from the last scattering surface all the way to future infinity. Furthermore given a specific model of inflation, using quantum field theory on curved space-times this history can be pushed \emph{back in time} to the epoch when space-time curvature was some 1062 times that at the horizon of a solar mass black hole! However, to extend the history further back to the Planck regime requires input from quantum gravity. An important aspect of this input is the choice of the background quantum geometry and of the Heisenberg state of cosmological perturbations thereon, motivated by Planck scale physics. This paper introduces first steps in that direction. Specifically we propose two principles that link quantum geometry and Heisenberg uncertainties in the Planck epoch with late time physics and explore in detail the observational consequences of the initial conditions they select. We find that the predicted temperature-temperature (T-T) correlations for scalar modes are indistinguishable from standard inflation at small angular scales even though the initial conditions are now set in the deep Planck regime. However, \emph{there is a specific power suppression at large angular scales}. As a result, the predicted spectrum provides a better fit to the PLANCK mission data than standard inflation, where the initial conditions are set in the general relativity regime. Thus, our proposal brings out a deep interplay between the ultraviolet and the infrared. Finally, the proposal also leads to specific predictions for power suppression at large angular scales also for the (T-E and E-E) correlations involving electric polarization. The PLANCK team is expected to release this data in the coming year.

http://arxiv.org/abs/1608.04461
Thermodynamics and the structure of quantum theory
Marius Krumm, Howard Barnum, Jonathan Barrett, Markus P. Mueller
(Submitted on 16 Aug 2016)
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Results in quantum gravity and general ideas of what a fundamental theory should look like suggest that thermodynamics plays a major role in the foundations of physics. In this paper, we address the question of which parts of quantum theory are already determined by compatibility with thermodynamics, and which aspects may still admit modification. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we generalize the concept of state majorization, crucial to recent work in fine-grained quantum thermodynamics, to this class of theories, study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin's notion of higher-order interference.

http://arxiv.org/abs/1608.04459
Entanglement as an axiomatic foundation for statistical mechanics
Giulio Chiribella, Carlo Maria Scandolo
(Submitted on 16 Aug 2016)
We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms---Causality, Purity Preservation, Pure Sharpness, and Purification---identify a class of theories where every mixed state can be modeled as the marginal of a pure entangled state and where every unsharp measurement can be modeled as a sharp measurement on a composite system. This class includes quantum theory and a number of alternative theories, such as quantum theory with real amplitudes, as well as a suitable extension of classical probability theory where classical systems can be combined with other non-classical systems. Theories satisfying our axioms support well-behaved notions of majorization, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle.

 

[kodama]

A note on the architecture of spacetime geometry
Fen Zuo
(Submitted on 20 Jul 2016)
Recently the SU(2) spin-network states in loop quantum gravity is generalized to those of the corresponding Kac-Moody algebra. We show that if one literally starts from the full SL(2,C) group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region. This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers. Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made.
Comments: 8 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1607.05866 [hep-th]
(or arXiv:1607.05866v1 [hep-th] for this version)

 

[kodama]

Spacetime-noncommutativity regime of Loop Quantum Gravity
Giovanni Amelino-Camelia, Malú Maira da Silva, Michele Ronco, Lorenzo Cesarini, Orchidea Maria Lecian
(Submitted on 2 May 2016)
A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by Loop-Quantum-Gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the κ-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1605.00497 [gr-qc]
(or arXiv:1605.00497v1 [gr-qc] for this version)

On the UV dimensions of Loop Quantum Gravity
Michele Ronco
(Submitted on 19 May 2016 (v1), last revised 28 Jul 2016 (this version, v4))
Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of spacetime dimensionality. Most of them rely on the \textit{spectral} dimension, others refer to the \textit{Hausdorff} dimension and, very recently, it has been introduced also the \textit{thermal} dimension. We here show that all these distinct definitions of dimension give the same outcome in the case of the effective regime of Loop Quantum Gravity (LQG). This is achieved by deriving a modified dispersion relation from the hypersurface-deformation algebra with quantum corrections. Moreover we also observe that the number of UV dimensions can be used to constrain the ambiguities in the choice of these LQG-based modifications of the Dirac spacetime algebra. In this regard, introducing the \textit{polymerization} of connections i.e. K→sin(δK)δ, we find that the leading quantum correction gives dUV=2.5. This result may indicate that the running to the expected value of two dimensions is ongoing, but it has not been completed yet. Finding dUV at ultra-short distances would require to go beyond the effective approach we here present.
Comments: Article ID 9897051, 7 pages. Advances in High Energy Physics (2016)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1155%2F2016%2F9897051&v=bb2c9ffe
Cite as: arXiv:1605.05979 [gr-qc]Phase Transition in Loop Quantum Gravity
Jarmo Mäkelä
(Submitted on 5 Apr 2016)
We point out that with a specific counting of states loop quantum gravity implies that black holes perform a phase transition at a certain characteristic temperature TC. In this phase transition the punctures of the spin network on the stretched horizon of the black hole jump, in effect, from the vacuum to the excited states. The characteristic temperature TC may be regarded as the lowest possible temperature of the hole. From the point of view of a distant observer at rest with respect to the hole the characteristic temperature TC corresponds to the Hawking temperature of the hole.
Comments: 7 pages, no figures, published in the Physical Review D. Comments welcome
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Phys. Rev. D 93, 084002 (2016)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevD%252E93%252E084002&v=f5697e8e
Cite as: arXiv:1604.01393 [gr-qc]

Vacuum CGHS in loop quantum gravity and singularity resolution
Alejandro Corichi, Javier Olmedo, Saeed Rastgoo
(Submitted on 22 Aug 2016)
We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog.
Comments: 27 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1608.06246 [gr-qc]

Teleparallel loop quantum cosmology in a system of intersecting branes
Alireza Sepehri, Anirudh Pradhan, A. Beesham, Jaume de Haro
(Submitted on 9 May 2016 (v1), last revised 7 Jun 2016 (this version, v2))
Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of teleparallel theory in a system of intersecting branes in M-theory in which the angle between them changes with time. This system is constructed by two intersecting anti-D8-branes, one compacted D4-brane and the other a D3-brane. These branes are built by joining M0-branes which develop in decaying fundamental strings. The compacted D4-brane is located between two intersecting anti-D8 branes and glues to one of them. Our universe is located on the D3 brane which wraps the D4 brane from one end and sticks to one of the anti-D8 branes from another one. In this system, there are three types of ?elds, corresponding to compacted D4 branes, intersecting branes and D3-branes. These ?elds interact with each other and make the angle between branes oscillate. By decreasing this angle and approaching the intersecting anti-D8 branes towards each other, the D4 brane rolls, the D3 brane wraps around the D4 brane, and t he universe contracts. By separating the intersecting branes and increasing the angle, the D4 brane rolls in the opposite direction, the D3 brane separates from it and the expansion branch begins. Also, the interaction between branes in this system gives us the exact form of the relevant Lagrangian for teleparallel LQC.
Comments: 11 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Phys.Lett.B760:94-100,2016
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1016%2Fj%252Ephysletb%252E2016%252E06%252E045&v=9b9a3abe
Cite as: arXiv:1605.02590 [gr-qc]

 

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http://arxiv.org/abs/1608.05947
Hybrid Models in Loop Quantum Cosmology
B. Elizaga Navascués, M. Martín-Benito, G.A. Mena Marugán
(Submitted on 21 Aug 2016)
In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes, and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid Loop Quantum Cosmology

 

[kodama]

Entropic corrected Newton's law of gravitation and the Loop Quantum Black Hole gravitational atom
R.G.L. Aragão, C.A.S.Silva
(Submitted on 16 Jan 2016)
One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. Loop quantum gravity is a theory that provide a way to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black holes or self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain the quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes. In order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.
Comments: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:1503.00559
Subjects: General Relativity and Quantum Cosmology (gr-qc)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1007%2Fs10714-016-2067-9&v=08ccf69c
Cite as: arXiv:1601.04993 [gr-qc]

 

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http://arxiv.org/abs/1608.06940
Operational General Relativity: Possibilistic, Probabilistic, and Quantum
Lucien Hardy
(Submitted on 24 Aug 2016)
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents' actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabilities and provide a compositional framework for calculating the probability of some operationally described situation. Finally we look at the quantum case. We review the operator tensor formulation of Quantum Theory and use it to set up an approach to Quantum Field Theory that is both operational and compositional. Then we consider strategies for solving the problem of Quantum Gravity. By referring only to operational quantities we are able to provide formulations for the possibilistic, probabilistic, and (the nascent) quantum cases that are manifestly invariant under diffeomorphisms.

 

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http://arxiv.org/abs/1608.07314
Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
Jibril Ben Achour, Suddhasattwa Brahma, Antonino Marciano
(Submitted on 25 Aug 2016)
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possesses a non closed (quantum) algebra of constraints once the holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as a signature change of the metric in the deep quantum region. We show in this paper that both those difficulties disappear when working with self dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.
[PLAIN]http://arxiv.org/abs/1608.07473[/PLAIN]
http://arxiv.org/abs/1608.07473
From physical symmetries to emergent gauge symmetries
Carlos Barceló, Raúl Carballo-Rubio, Francesco Di Filippo, Luis J. Garay
(Submitted on 26 Aug 2016)
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

 

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http://arxiv.org/abs/1608.07772
Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
John L. Dupuy, Parampreet Singh
(Submitted on 28 Aug 2016)
The spatially closed Friedmann-Lemaitre-Robertson-Walker model in loop quantum cosmology admits two inequivalent consistent quantizations: one based on expressing field strength in terms of holonomies over closed loops, and, another using a connection operator and open holonomies. Using effective dynamics, we investigate the phenomenological differences between the two quantizations for single fluid and two fluid scenarios with various equations of state, including phantom matter. We show that a striking difference between the two quantizations is the existence of two distinct quantum turnarounds, either bounces or recollapses, in the connection quantization, in contrast to a single distinct quantum bounce or recollapse in the holonomy quantization. These results generalize an earlier result on two distinct quantum bounces for stiff matter by Corichi and Karami. However, we find that in certain situations two distinct quantum turnarounds can become virtually indistinguishable. And depending on initial conditions, a pure quantum cyclic universe can also exist undergoing quantum bounce and a quantum recollapse. We show that for various equations of states, connection based quantization leads to super-Planckian values of the energy density and the expansion scalar at quantum turnarounds. Interestingly, we find that very extreme energy densities can also occur for holonomy quantization, breaching the maximum allowed density in spatially flat loop quantized model. However, the expansion scalar in all these cases is bounded by a universal value.

http://arxiv.org/abs/1608.07971
Towards a Hartle-Hawking state for loop quantum gravity
Satya Dhandhukiya, Hanno Sahlmann
(Submitted on 29 Aug 2016)
The Hartle-Hawking state is a proposal for a preferred initial state for quantum gravity, based on a path integral over all compact Euclidean four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the (Lorentzian) Hamiltonian constraint of general relativity in ADM variables in a formal sense. In this article we mimic this procedure of constructing an initial state in terms of Ashtekar-Barbero variables, and observe that the wave function thus constructed does not satisfy the Lorentzian Hamiltonian constraint even in a formal sense. We also investigate this issue for the relativistic particle. We finally suggest a modification of the proposal that does satisfy the constraint at least in a formal sense and start to consider its implications in quantum cosmology.

http://arxiv.org/abs/1608.07826
From Conformal to Einstein Gravity
Giorgos Anastasiou, Rodrigo Olea
(Submitted on 28 Aug 2016)
We provide a simple derivation of the equivalence between Einstein and Conformal Gravity (CG) with Neumann boundary conditions given by Maldacena. As Einstein spacetimes are Bach flat, a generic solution to CG would contain both Einstein and non-Einstein part. Using this decomposition of the spacetime curvature in the Weyl tensor, makes manifest the equivalence between the two theories, both at the level of the action and the variation of it. As a consequence, we show that the on-shell action for Critical Gravity in four dimensions is given uniquely in terms of the Bach tensor.

 

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http://arxiv.org/abs/1609.00207
Gravitational action with null boundaries
Luis Lehner, Robert C. Myers, Eric Poisson, Rafael D. Sorkin
(Submitted on 1 Sep 2016)
We present a complete discussion of the boundary term in the action functional of general relativity when the boundary includes null segments in addition to the more usual timelike and spacelike segments. We confirm that ambiguities appear in the contribution from a null segment, because it depends on an arbitrary choice of parametrization for the generators. We also show that similar ambiguities appear in the contribution from a codimension-two surface at which a null segment is joined to another (spacelike, timelike, or null) segment. The parametrization ambiguity can be tamed by insisting that the null generators be affinely parametrized; this forces each null contribution to the boundary action to vanish, but leaves intact the fredom to rescale the affine parameter by a constant factor on each generator. Once a choice of parametrization is made, the ambiguity in the joint contributions can be eliminated by formulating well-motivated rules that ensure the additivity of the gravitational action. Enforcing these rules, we calculate the time rate of change of the action when it is evaluated for a so-called "Wheeler-deWitt patch" of a black hole in asymptotically-anti de Sitter space. We recover a number of results cited in the literature, obtained with a less complete analysis.

 

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http://arxiv.org/abs/1609.01725
The Good, the Bad, and the Ugly of Gravity and Information
Gerard 't Hooft, Steven B. Giddings, Carlo Rovelli, Piero Nicolini, Jonas Mureika, Matthias Kaminski, Marcus Bleicher
(Submitted on 6 Sep 2016)
Various contenders for a complete theory of quantum gravity are at odds with each other. This is in particular seen in the ways they relate to information and black holes, and how to effectively treat quantization of the background spacetime. Modern perspectives on black hole evaporation suggest that quantum gravity effects in the near-horizon region can perturb the local geometry. The approaches differ, however, in the time scale on which one can expect these effects to become important. This panel session presents three points of view on these problems, and considers the ultimate prospect of observational tests in the near future.

 

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http://arxiv.org/abs/1609.02159
Quantum-gravity phenomenology with primordial black holes
Francesca Vidotto, Aurelien Barrau, Boris Bolliet, Marrit Shutten, Celine Weimer
(Submitted on 7 Sep 2016)
Quantum gravity may allow black holes to tunnel into white holes. If so, the lifetime of a black hole could be shorter than the one given by Hawking evaporation, solving the information paradox. More interestingly, this could open to a new window for quantum-gravity phenomenology, in connection with the existence of primordial black holes. We discuss in particular the power of the associated explosion and the possibility to observe an astrophysical signal in the radio and in the gamma wavelengths.

http://arxiv.org/abs/1609.02219
Loop expansion and the bosonic representation of loop quantum gravity
Eugenio Bianchi, Jonathan Guglielmon, Lucas Hackl, Nelson Yokomizo
(Submitted on 7 Sep 2016)
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent, heat kernel and squeezed states.
[PLAIN]http://arxiv.org/abs/1609.02429[/PLAIN]
http://arxiv.org/abs/1609.02429
Coarse graining flow of spin foam intertwiners
Bianca Dittrich, Erik Schnetter, Cameron J. Seth, Sebastian Steinhaus
(Submitted on 8 Sep 2016)
Simplicity constraints play a crucial role in the construction of spin foam models, yet their effective behaviour on larger scales is scarcely explored. In this article we introduce intertwiner and spin net models for the quantum group SU(2)k×SU(2)k, which implement the simplicity constraints analogous to 4D Euclidean spin foam models, namely the Barrett-Crane (BC) and the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) model. These models are numerically coarse grained via tensor network renormalization, allowing us to trace the flow of simplicity constraints to larger scales. In order to perform these simulations we have substantially adapted tensor network algorithms, which we discuss in detail.
The BC and the EPRL/FK model behave very differently under coarse graining: While the unique BC intertwiner model is a fixed point and therefore constitutes a 2D topological phase, BC spin net models flow away from the initial simplicity constraints and converge to several different topological phases. Most of these phases correspond to decoupling spin foam vertices, however we find also a new phase in which this is not the case, and in which a non-trivial version of the simplicity constraints holds. The coarse graining flow of the BC spin net models indicates furthermore that the phase transitions are not of second order. The EPRL/FK model by contrast reveals a far more intricate and complex dynamics. We observe an immediate flow away from the original simplicity constraints, however, with the truncation employed here, the models generically do not converge to a fixed point.
The results show that the imposition of simplicity constraints can indeed lead to interesting and complex dynamics. Thus we will need to further develop coarse graining tools to efficiently study the large scale behaviour of spin foam models, in particular for the EPRL/FK model.

 

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http://arxiv.org/abs/1609.03524
A conformal model of gravitons
John F. Donoghue
(Submitted on 12 Sep 2016)
In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running coupling. When running from high energy, the coupling gets large at a scale which can be called the Planck mass. If the Lorentz connection is confined at that scale, the low energy theory can have the Einstein Lagrangian induced at low energy through dimensional transmutation. However, in general there will be new divergences in such a theory and the Lagrangian basis should be expanded. I construct a conformally invariant model with a larger basis size which potentially may have the same property.

 

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http://arxiv.org/abs/1609.04028
Conformal loop quantum gravity coupled to the Standard Model
Miguel Campiglia, Rodolfo Gambini, Jorge Pullin
(Submitted on 13 Sep 2016)
We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge fixing and a modified Higgs mechanism particles acquire mass and one recovers general relativity coupled to the Standard Model. The theory suggests new views with respect to the definition of the Hamiltonian constraint in loop quantum gravity, the semi-classical limit and the issue of finite renormalization in quantum field theory in quantum space-time. It also gives hints about the elimination of ambiguities that arise in quantum field theory in quantum space-time in the calculation of back-reaction.

 

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http://arxiv.org/abs/1609.04806
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Clement Delcamp, Bianca Dittrich, Aldo Riello
(Submitted on 15 Sep 2016)
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non--Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non--Abelian analogue of the `magnetic centre choice', as obtained through an extended--Hilbert--space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement theory can be related to a choice of (squeezed) vacuum state.

 

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http://arxiv.org/abs/1609.04813
Quantum gravity on foliated spacetime - asymptotically safe and sound
Jorn Biemans, Alessia Platania, Frank Saueressig
(Submitted on 15 Sep 2016)
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ϵ-expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

 

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http://arxiv.org/abs/1609.06439
Invitation to random tensors
Razvan Gurau
(Submitted on 21 Sep 2016)
Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field.
This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.

 

[kodama]

Proof of Bekenstein-Mukhanov ansatz in loop quantum gravity
Abhishek Majhi
(Submitted on 22 Sep 2016)
A simple proof of Bekenstein-Mukhanov(BM) ansatz is given within the loop quantum gravity(LQG) framework. The macroscopic area of an equilibrium black hole horizon indeed manifests a linear quantization. The quantum number responsible for this discreteness of the macroscopic area has a physical meaning in the LQG framework, unlike the ad hoc one that remained unexplained in BM ansatz.
Comments: 5 pages, close to published version
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Mod. Phys. Lett. A, Vol. 31, No. 31 (2016) 1650171
DOI: 10.1142/S0217732316501716
Cite as: arXiv:1609.07125 [gr-qc]

 

[kodama]

Non-compact groups, tensor operators and applications to quantum gravity
Giuseppe Sellaroli
(Submitted on 25 Sep 2016)
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to generalise the Wigner-Eckart theorem to non-compact groups. The result relies on the knowledge of the recoupling theory between finite-dimensional and infinite-dimensional irreducible representations of the group; here the previously unconsidered cases of the 3D and 4D Lorentz groups are investigated in detail. As an application, the Wigner-Eckart theorem is used to generalise the Jordan-Schwinger representation of SU(2) to both groups, for all representation classes. Next, the results obtained for the 3D Lorentz group are applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the well-known spinorial approach used in the Euclidean case. Tensor operators are used to construct observables and to generalise the Hamiltonian constraint introduced by Bonzom and Livine (2012) for 3D gravity to the Lorentzian case. The Ponzano-Regge amplitude is shown to be a solution of this constraint by recovering the (opportunely generalised) Biedenharn-Elliott relations. Finally, the focus is shifted on the intertwiner space based on SU(2) representations, widely used in loop quantum gravity. When working in the spinorial formalism, it has been shown that the Hilbert space of n-valent intertwiners with fixed total area is a representation of U(n). Here it is shown that the full space of all n-valent intertwiners forms an irreducible representation of the non-compact group SO*(2n). This fact is used to construct a new kind of coherent intertwiner state (in the sense of Perelomov). Hints of how these coherent states can be interpreted in the semi-classical limit as convex polyhedra are provided.
Comments: PhD thesis. Single sided version and original source files included in the gzipped tar. Abstract was shortened to comply with the arXiv's 1920 characters limitation
Subjects: Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Representation Theory (math.RT)
Cite as: arXiv:1609.07795 [math-ph]

Light-like Scattering in Quantum Gravity
N. E. J. Bjerrum-Bohr, John F. Donoghue, Barry R. Holstein, Ludovic Plante, Pierre Vanhove
(Submitted on 23 Sep 2016)
We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin-1/2, spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum hbar dependent terms using the same eikonal method.
Comments: latex 31 pages. 5 feynmp figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Report number: IPHT-t16/082, ACFI-T16-23
Cite as: arXiv:1609.07477 [hep-th]

Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)
Matthew J. Lake
(Submitted on 13 Jul 2016)
We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical) energy-momentum relation. In canonical QM, this yields a dispersion relation involving ℏ but not c, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing G and c, and associated commutators involving ℏ. This naturally defines a "wave-gravity duality", suggesting that a quantum wave packet describing {\it self-gravitating matter} obeys a dispersion relation involving G, c and ℏ. We propose an ansatz for this relation, which is valid in the semi-Newtonian regime of both QM and general relativity. In this limit, space and time are absolute, but imposing vmax=c allows us to recover the standard expressions for the Compton wavelength λC and the Schwarzschild radius rS within the same ontological framework. The new dispersion relation is based on "extended" de Broglie relations, which remain valid for slow-moving bodies of {\it any} mass m. These reduce to canonical form for m≪mP, yielding λC from the standard uncertainty principle, whereas, for m≫mP, we obtain rS as the natural radius of a self-gravitating quantum object. Thus, the extended de Broglie theory naturally gives rise to a unified description of black holes and fundamental particles in the semi-Newtonian regime.
Comments: 38 pages, 5 figures. Submitted to the Universe special issue "Open questions in black hole physics"
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1607.03689 [gr-qc]

A Tree-level Unitary Noncompact Weyl-Einstein-Yang-Mills Model
Suat Dengiz
(Submitted on 8 Sep 2016)
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3+1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable constant curvature vacuum. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2−1 massless scalar bosons, N2−1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated. Throughout the unitarity analysis, we notice that one actually has two distinct candidates for vacuum field equation: in the first choice, the classical cosmological constant and vacuum expectation value of scalar fields are related whereas, in the second choice, the scalar bosons and trace of graviton are related such that the scalar bosons develop a repulsive interaction.
Comments: 19 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Report number: MIT-CTP-4834
Cite as: arXiv:1609.02475 [hep-th]

∞−∞: vacuum energy and virtual black-holes
Andrea Addazi
(Submitted on 27 Jul 2016 (v1), last revised 4 Aug 2016 (this version, v5))
We discuss other contributions to the vacuum energy of quantum field theories and quantum gravity, which have not been considered in literature. As is well known, the presence of virtual particles in vacuum provides the so famous and puzzling contributions to the vacuum energy. As is well known, these mainly come from loop integrations over the four-momenta space. However, we argue that these also imply the presence of a mass density of virtual particles in every volume cell of space-time. The most important contribution comes from quantum gravity S2×S2 bubbles, corresponding to virtual black hole pairs. The presence of virtual masses could lead to another paradox: the space-time itself would have an intrinsic virtual mass density contribution leading to a disastrous contraction - as is known, no negative masses exist in general relativity. We dub this effect {\it the cosmological problem of second type}: if not other counter-terms existed, the vacuum energy would be inevitably destabilized by virtual-mass contributions. It would be conceivable that the cosmological problem of second type could solve the first one. Virtual masses renormalize the vacuum energy to an unpredicted parameter, as in the renormalization procedure of the Standard Model charges. In the limit of MPl→∞ (Pauli-Villars limit), virtual black holes have a mass density providing an infinite counter-term to the vacuum energy divergent contribution MPl→∞ (assuming MUV=MPl). Therefore, in the same Schwinger-Feynman-Tomonaga attitude, the problem of a divergent vacuum energy could be analogous to the {\it put-by-hand} procedure used for Standard Model parameters.
Comments: More useful references added in Section II A & Conclusions, few english typos and typo in Eq.29 were corrected, more acknowledgments added. Conclusions are unchanged
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1607.08107 [hep-th]

 

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https://arxiv.org/abs/1609.09110
A Bilocal Model for the Relativistic Spinning Particle
Trevor Rempel, Laurent Freidel
(Submitted on 28 Sep 2016)
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a non-relativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles with the restriction that the quantum spin has to be an integer.

 

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https://arxiv.org/abs/1610.01142
Spin on a 4D Feynman Checkerboard
Brendan Z. Foster, Ted Jacobson
(Submitted on 4 Oct 2016)
We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the step direction, while for left-handed it is the orthogonal projector. Iteration yields a path integral for the retarded propagator, with matrix path amplitude proportional to the product of projection operators. This assigns the amplitude i±T3−B/22−N to a path with N steps, B bends, and T right-handed minus left-handed bends, where the sign corresponds to the chirality. Fermion doubling does not occur in this discrete scheme. A Dirac mass m introduces the amplitude iϵm to flip chirality in any given time step ϵ, and a Majorana mass similarly introduces a charge conjugation amplitude.

https://arxiv.org/abs/1610.01457
Self-Dual Gravity
Kirill Krasnov
(Submitted on 5 Oct 2016)
Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant. Nevertheless, this theory is not only renormalisable but quantum finite, as we explain. We also collect various facts about self-dual gravity that are scattered across the literature.

 

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https://arxiv.org/abs/1610.02020
BF gravity
Mariano Celada, Diego González, Merced Montesinos
(Submitted on 6 Oct 2016)
BF gravity comprises all the formulations of gravity that are based on deformations of BF theory. Such deformations consist of either constraints or potential terms added to the topological BF action that turn some of the gauge degrees of freedom into physical ones, particularly giving rise to general relativity. The BF formulations have provided new and deep insights into many classical and quantum aspects of the gravitational field, setting the foundations for the approach to quantum gravity known as spinfoam models. In this review, we present a self-contained and unified treatment of the BF formulations of D-dimensional general relativity and other related models, focusing on the classical aspects of them and including some new results.

 

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Four principles for quantum gravity
Lee Smolin
(Submitted on 6 Oct 2016)
Four principles are proposed to underlie the quantum theory of gravity. We show that these suffice to recover the Einstein equations. We also suggest that MOND results from a modification of the classical equivalence principle, due to quantum gravity effects.
Comments: 26 pages, one figure and caption taken from McGaugh, Lelli, Schombert, arXiv:1609.05917v1
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1610.01968 [gr-qc]
(or arXiv:1610.01968v1 [gr-qc] for this version)

 

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https://arxiv.org/abs/1610.02134
Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
Muxin Han, Ling-Yan Hung
(Submitted on 7 Oct 2016)
The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space Σ with boundary ∂Σ is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region A and its complement A¯ are specified on the boundary ∂Σ, we show that the boundary entanglement entropy S(A) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. S(A) is proportional to the minimal area of the bulk surface attached to the boundary of A in ∂Σ.

https://arxiv.org/abs/1610.02343
Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
Yannick Herfray
(Submitted on 7 Oct 2016)
This paper establishes the relation between traditional results from (euclidean) twistor theory and chiral formulations of General Relativity, especially the pure connection formulation. Starting from a SU(2)-connection only we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear-graviton theorem. Finally we discuss what new strategies this "connection approach" to twistors suggests for constructing a twistor action for gravity. In appendix we also review all known chiral Lagrangians for GR.

 

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https://arxiv.org/abs/1610.02408
A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
Joshua H. Cooperman, Kyle Lee, Jonah M. Miller
(Submitted on 7 Oct 2016)
Studying transition amplitudes in (2+1)-dimensional causal dynamical triangulations, Cooperman and Miller discovered speculative evidence for Lorentzian quantum geometries emerging from its Euclidean path integral. On the basis of this evidence, Cooperman and Miller conjectured that Lorentzian de Sitter spacetime, not Euclidean de Sitter space, dominates the ground state of the quantum geometry of causal dynamical triangulations on large scales, a scenario akin to that of the Hartle-Hawking no-boundary proposal in which Lorentzian spacetimes dominate a Euclidean path integral. We argue against this conjecture: we propose a more straightforward explanation of their findings, and we proffer evidence for the Euclidean nature of these seemingly Lorentzian quantum geometries. This explanation reveals another manner in which the Euclidean path integral of causal dynamical triangulations behaves correctly in its semiclassical limit--the implementation and interaction of multiple constraints.

https://arxiv.org/abs/1610.02533
Loop Quantum Cosmology Gravitational Baryogenesis
S.D. Odintsov, V.K. Oikonomou
(Submitted on 8 Oct 2016)
Loop Quantum Cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer remedy or modify various classical cosmology aspects. In this paper we address the gravitational baryogenesis mechanism in the context of Loop Quantum Cosmology. As we demonstrate, when Loop Quantum Cosmology effects are taken into account in the resulting Friedmann equations for a flat Friedmann-Robertson-Walker Universe, then even for a radiation dominated Universe, the predicted baryon-to-entropy ratio from the gravitational baryogenesis mechanism is non-zero, in contrast to the Einstein-Hilbert case, in which case the baryon-to-entropy ratio is zero. We also discuss various other cases apart from the radiation domination case, and we discuss how the baryon-to-entropy ratio is affected from the parameters of the quantum theory. In addition, we use illustrative exact solutions of Loop Quantum Cosmology and we investigate under which circumstances the baryon-to-entropy ratio can be compatible with the observational constraints.

https://arxiv.org/abs/1610.02716
3d Quantum Gravity: Coarse-Graining and q-Deformation
Etera R. Livine
(Submitted on 9 Oct 2016)
The Ponzano-Regge state-sum model provides a quantization of 3d gravity as a spin foam, providing a quantum amplitude to each 3d triangulation defined in terms of the 6j-symbol (from the spin-recoupling theory of SU(2) representations). In this context, the invariance of the 6j-symbol under 4-1 Pachner moves, mathematically defined by the Biedenharn-Elliot identity, can be understood as the invariance of the Ponzano-Regge model under coarse-graining or equivalently as the invariance of the amplitudes under the Hamiltonian constraints. Here we look at length and volume insertions in the Biedenharn-Elliot identity for the 6j-symbol, derived in some sense as higher derivatives of the original formula. This gives the behavior of these geometrical observables under coarse-graining. These new identities turn out to be related to the Biedenharn-Elliot identity for the q-deformed 6j-symbol and highlight that the q-deformation produces a cosmological constant term in the Hamiltonian constraints of 3d quantum gravity.

 

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https://arxiv.org/abs/1610.04462
Causal spin foams
Giorgio Immirzi
(Submitted on 14 Oct 2016)
I discuss how to impose causality on spin-foam models, separating forward and backward propagation, turning a given triangulation to a 'causal set', and giving asymptotically the exponential of the Regge action, not a cosine. I show the equivalence of the prescriptions which have been proposed to achieve this. Essential to the argument is the closure condition for the 4-simplices, all made of space-like tetrahedra.

 

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https://arxiv.org/abs/1610.06532
Uncertainty Principle in Loop Quantum Cosmology by Moyal Formalism
Leonid Perlov
(Submitted on 20 Oct 2016)
In this paper we derive the uncertainty principle for the Loop Quantum Cosmology homogeneous and isotropic FLWR model with the holonomy-flux algebra. In our derivation we use the Wigner-Moyal-Groenewold phase space formalism. The formalism uses the characteristic functions and the Wigner transform, which maps the quantum operators to the functions on the phase space. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the Quantum Mechanics. One can derive from it both the canonical and path integral QM as well as the uncertainty principle. In this paper we apply the phase-space formalism to the quantum cosmology holonomy-flux algebra in case of the homogeneous and isotropic space to obtain the Loop Quantum Cosmology uncertainty principle.

 

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https://arxiv.org/abs/1610.07467
A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables
Jibril Ben Achour, Suddhasattwa Brahma, Julien Grain, Antonino Marciano
(Submitted on 24 Oct 2016)
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. This work extends a similar result obtained in the context of spherically symmetric gravity coupled to a scalar field, suggesting that self dual variables could be better suited than their real counterparts to treat inhomogeneous LQG models.

 

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https://arxiv.org/abs/1610.08840
Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
Martin Bojowald, Suddhasattwa Brahma
(Submitted on 27 Oct 2016)
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are included.

https://arxiv.org/abs/1610.08850
Signature change in 2-dimensional black-hole models of loop quantum gravity
Martin Bojowald, Suddhasattwa Brahma
(Submitted on 27 Oct 2016)
Signature change has been identified as a generic consequence of holonomy modifications in spherically symmetric models of loop quantum gravity with real connections, which includes modified Schwarzschild solutions. Here, this result is extended to 2-dimensional dilaton models and to different choices of canonical variables, including in particular the Callan-Giddings-Harvey-Strominger (CGHS) solution. New obstructions are found to coupling matter and to including operator-ordering effects in an anomaly-free manner.

 

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https://arxiv.org/abs/1610.09864
The information recovery problem
Valentina Baccetti, Viqar Husain, Daniel R. Terno
(Submitted on 31 Oct 2016)
The problem of rescuing unitary matter evolution on a black hole spacetime remains unresolved. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element --- forming of the event horizon before the evaporation begins --- is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.

https://arxiv.org/abs/1610.09681
Asymptotically Safe Grand Unification
Borut Bajc, Francesco Sannino
(Submitted on 30 Oct 2016)
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

 

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https://arxiv.org/abs/1611.00785
The Geometry of Small Causal Cones
Ian Jubb
(Submitted on 2 Nov 2016)
We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike hypersurface. We also consider a scalar field on the causal set, and obtain causal set expressions relating to its normal derivatives with respect to the hypersurface.

 

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Emergent Gravity and the Dark Universe
Erik P. Verlinde
(Submitted on 7 Nov 2016 (v1), last revised 8 Nov 2016 (this version, v2))
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Comments: 5 figures
Subjects: High Energy Physics - Theory (hep-th)
Cite as: arXiv:1611.02269 [hep-th]

 

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https://arxiv.org/abs/1611.03668
The loop gravity string
Laurent Freidel, Alejandro Perez, Daniele Pranzetti
(Submitted on 11 Nov 2016)
In this work we study canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge c=3. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary SU(2) gauge symmetry is recovered via the action of the U(1)3 Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation. We finally show that this symmetry is broken by the presence of background curvature.

 

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https://arxiv.org/abs/1604.07818
Comments on the Sachdev-Ye-Kitaev model
Juan Maldacena, Douglas Stanford
(Submitted on 26 Apr 2016)
We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field.
The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2,R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry.
This article is largely based on talks given by Kitaev \cite{KitaevTalks}, which motivated us to work out the details of the ideas described there.

https://arxiv.org/abs/1601.06768
The Spectrum in the Sachdev-Ye-Kitaev Model
Joseph Polchinski, Vladimir Rosenhaus
(Submitted on 25 Jan 2016)
The SYK model consists of N≫1 fermions in 0+1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the Schwinger-Dyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.

https://arxiv.org/abs/1610.09758
An SYK-Like Model Without Disorder
Edward Witten
(Submitted on 31 Oct 2016 (v1), last revised 3 Nov 2016 (this version, v2))
Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large n limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further probes of this approach to holographic duality.

https://arxiv.org/abs/1611.04032
The complete 1/N expansion of a SYK--like tensor model
Razvan Gurau
(Submitted on 12 Nov 2016)
A SYK--like model close to the colored tensor models has recently been proposed \cite{Witten:2016iux}. Building on results obtained in tensor models \cite{GurSch}, we discuss the complete 1/N expansion of the model. We detail the two and four point functions at leading order. The leading order two point function is a sum over melonic graphs, and the leading order relevant four point functions are sums over dressed ladder diagrams. We then show that any order in the 1/N series of the two point function can be written solely in term of the leading order two and four point functions. The full 1/N expansion of arbitrary correlations can be obtained by similar methods.

 

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https://arxiv.org/abs/1611.05315
General Covariance from the Quantum Renormalization Group
Vasudev Shyam
(Submitted on 15 Nov 2016)
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the D+1 dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the D dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of gradient form.

https://arxiv.org/abs/1611.05325
Transition probability spaces in loop quantum gravity
Xiao-Kan Guo
(Submitted on 15 Nov 2016)
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is achieved by first checking such structures in covariant quantum mechanics, and then passing to spin foam models via the general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the Hilbert space of the canonical theory and the relevant quantum logical structure. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize property transitions and causality in this categorical context in connection with presheaves on quantaloids and respectively causal categories. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.

 

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https://arxiv.org/abs/1611.07009
Testing Quantum Black Holes with Gravitational Waves
Valentino F. Foit, Matthew Kleban
(Submitted on 21 Nov 2016)
We argue that near-future detections of gravity waves from merging black hole binaries will either confirm or conclusively rule out a long-standing proposal, originally due Bekenstein and Mukhanov, that the areas of black hole horizons are quantized in integer multiples of the Planck area times an O(1) constant \alpha. A single measurement of the "ring down" phase after a binary merger, if consistent with the predictions of classical general relativity, will rule out most or all (depending on the spin of the hole) of the extant proposals in the literature for the value of \alpha. A measurement of two such events for final black holes with substantially different spins will rule out the proposal for any \alpha.