Loop-and-allied QG bibliography

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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.

 

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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]

 

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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.

 

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https://arxiv.org/abs/1611.07849
General Relativity from Three-Forms in Seven Dimensions
Kirill Krasnov
(Submitted on 23 Nov 2016)
We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian. Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of S^3. Realistic values of Lambda correspond to S^3 of Planck size.

 

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https://arxiv.org/abs/1611.08915
Uncolored Random Tensors, Melon Diagrams, and the SYK Models
Igor R. Klebanov, Grigory Tarnopolsky
Comments: 23 pages, 18 figures
Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possesses a novel large $N$ limit, where $g^(2)N^{3}$ is held fixed. In this limit the perturbative expansion in the quartic coupling constant, $g$, is dominated by a special class of "melon" diagrams. We study "uncolored" models of this type, which contain a single copy of real rank-$3$ tensor. Its three indexes are distinguishable; therefore, the models possesses $O(N)^{3}$ symmetry with the tensor field transforming in the tri-fundamental representation. Such uncolored models also possesses the large $N$ limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting tensor therefore has a similar large N limit to the model recently introduced by Witten as an implementation of the Sachdev-Ye-Kitaev (SYK) model which does not require disorder. Gauging the $O(N)^{3}$ symmetry in our quantum mechanical model removes the non-singlet states; therefore, one can search for its well-defined gravity dual. We point out, however, that the model possesses a vast number of gauge-invariant operators involving higher powers of the tensor field, suggesting that the complete gravity dual will be intricate. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor, which has $U(N)^{2}×O(N)$ symmetry and argue that it is equivalent in the large $N$ limit to a version of SYK model with complex fermions. Finally, we discuss similar models of a commuting tensor in dimension $d$. While the quartic interaction is not positive definite, we construct the large N Schwinger-Dyson equation for the two-point function and show that its solution is consistent with conformal invariance. We carry out a perturbative check of this result using the $4−\epsilon$ expansion.

 

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https://arxiv.org/abs/1611.09810
Phenomenology with fluctuating quantum geometries in loop quantum cosmology
Ivan Agullo, Abhay Ashtekar, Brajesh Gupt
(Submitted on 29 Nov 2016)
The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lema\^{i}tre, Robertson, Walker) \emph{quantum} geometry, we allow `widely spread' states in which the \emph{relative} dispersions are as large as 168% in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum PR(k) and the spectral index ns(k) of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final PR(k) and ns(k): Within observational error bars, their effect is degenerate with a different freedom in the theory, namely the number of \emph{pre-inflationary} e-folds NB⋆ between the bounce and the onset of inflation. Therefore, with regard to observational consequences, one can simulate the freedom in the choice of states with large fluctuations in the Planck era using the simpler, sharply peaked states, simply by allowing for different values of NB⋆.

 

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https://arxiv.org/abs/1611.10281
Entanglement Entropy in Causal Set Theory
Rafael D. Sorkin, Yasaman K. Yazdi
(Submitted on 30 Nov 2016)
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Defining entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which definitions of entanglement typically rely is not available in a causal set. Instead, we will appeal to a more global expression given in arXiv:1205.2953 which, for a gaussian scalar field, expresses the entropy of a spacetime region in terms of the field's correlation function within that region. Carrying this formula over to the causal set, one obtains an entanglement entropy which is both finite and of a Lorentz invariant nature. Herein we evaluate this entropy for causal sets of 1+1 dimensions, and specifically for order-intervals ("causal diamonds") within the causal set, finding in the first instance an entropy that obeys a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one can obtain an area law by truncating the eigenvalues of a certain "Pauli-Jordan" operator that enters into the entropy formula. In connection with these results, we also study the "entropy of coarse-graining" generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, "universal" behaviour in both cases.

 

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https://arxiv.org/abs/1612.00266
Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons
Jahed Abedi, Hannah Dykaar, Niayesh Afshordi
(Submitted on 1 Dec 2016)
In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for observational signatures of these echoes in the gravitational wave data released by advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), following the three black hole merger events GW150914, GW151226, and LVT151012. In particular, we look for repeating damped echoes with time-delays of 8MlogM (+spin corrections, in Planck units), corresponding to Planck-scale departures from GR near their respective horizons. Accounting for the "look elsewhere" effect due to uncertainty in the echo template, we find tentative evidence for Planck-scale structure near black hole horizons at 2.9σ significance level (corresponding to false detection probability of 1 in 270). Future data releases from LIGO collaboration, along with more physical echo templates, will definitively confirm (or rule out) this finding, providing possible empirical evidence for alternatives to classical black holes, such as in firewall or fuzzball paradigms.

https://arxiv.org/abs/1612.00324
Quantum reduced loop gravity: extension to gauge vector field
Jakub Bilski, Emanuele Alesci, Francesco Cianfrani, Pietro Donà, Antonino Marciano
(Submitted on 1 Dec 2016)
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step towards deriving the full quantum gravity corrections to the vector field semiclassical dynamics.

https://arxiv.org/abs/1612.00353
Time in quantum cosmology
Martin Bojowald, Theodore Halnon
(Submitted on 1 Dec 2016)
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations from a single deparameterized model if quantum corrections from fluctuations and higher moments are included. The framework of effective constraints shows how proper-time evolution can consistently be defined in quantum cosmological systems, such that it is time reparameterization invariant when compared with other choices of coordinate time. At the same time, it allows transformations of moment corrections in different deparameterizations of the same model, indicating partial time reparameterization of internal-time evolution. However, in addition to corrections from moments such as quantum fluctuations, also factor ordering corrections may appear. The latter generically break covariance in internal-time formulations. Fluctuation effects in quantum cosmology are therefore problematic, in particular if derivations are made with a single choice of internal time or a fixed physical Hilbert space.

 

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https://arxiv.org/abs/1612.00551
A Classical and Spinorial Description of the Relativistic Spinning Particle
Trevor Rempel, Laurent Freidel
(Submitted on 2 Dec 2016)
In a previous work we showed that spin can be envisioned as living in a phase space that is dual to the standard phase space of position and momentum. In this work we demonstrate that the second class constraints inherent in this "Dual Phase Space" picture can be solved by introducing a spinorial parameterization of the spinning degrees of freedom. This allows for a purely first class formulation that generalizes the usual relativistic description of spinless particles and provides several insights into the nature of spin and its relationship with spacetime and locality. In particular, we find that the spin motion acts as a Lorentz contraction on the four-velocity and that, in addition to proper time, spinning particles posses a second gauge invariant observable which we call proper angle. Heuristically, this proper angle represents the amount of Zitterbewegung necessary for a spin transition to occur. Additionally, we show that the spin velocity satisfies a causality constraint, and even more stringently, that it is constant along classical trajectories. This leads to the notion of "half-quantum" states which violate the classical equations of motion, and yet do not experience an exponential suppression in the path integral. Finally we give a full analysis of the Poisson bracket structure of this new parametrization.

 

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https://arxiv.org/abs/1612.01084
Causal structures in cosmology
George Ellis, Jean-Philippe Uzan
(Submitted on 4 Dec 2016)
This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.

https://arxiv.org/abs/1612.01236
Loop Quantum Cosmology: A brief review
Ivan Agullo, Parampreet Singh
(Submitted on 5 Dec 2016)
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics. These include the problem of singularities and their possible generic resolution, constructing viable non-singular models of the very early universe, and bridging quantum gravity with cosmological observations. These results, which emerge from an interplay of sophisticated analytical and numerical techniques, has also led to valuable hints on loop quantization of black hole and inhomogeneous spacetimes. In this review, we provide a summary of this progress while focusing on concrete examples of the quantization procedure and phenomenology of cosmological perturbations.

https://arxiv.org/abs/1612.01296
Conformal anomalies and the Einstein Field Equations
Hadi Godazgar, Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 5 Dec 2016)
We compute corrections to the Einstein field equations which are induced by the anomalous effective actions associated to the type A conformal anomaly, both for the (non-local) Riegert action, as well as for the local action with dilaton. In all cases considered we find that these corrections can be very large.

 

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https://arxiv.org/abs/1612.01952
Why Our Universe is Comprehensible
James B. Hartle
(Submitted on 6 Dec 2016)
Einstein wrote memorably that `The eternally incomprehensible thing about the world is its comprehensibility.' This paper argues that the universe must be comprehensible at some level for information gathering and utilizing subsystems such as human observers to evolve and function.

 

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https://arxiv.org/abs/1612.03851
A Supersymmetric SYK-like Tensor Model
Cheng Peng, Marcus Spradlin, Anastasia Volovich
(Submitted on 12 Dec 2016)
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, "quarks" and "mesons". We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic "melon" diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

 

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https://arxiv.org/abs/1612.04002
Self-Dual Gravity and the Immirzi parameter
Javier Chagoya, M. Sabido
(Submitted on 13 Dec 2016)
Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions introduced by Witten in the description of (2+1) gravity as a gauge theory. This relation had been conjectured previously in the literature, but not derived.

https://arxiv.org/abs/1612.04334
Echoes of chaos from string theory black holes
Vijay Balasubramanian, Ben Craps, Bartłomiej Czech, Gábor Sárosi
(Submitted on 13 Dec 2016)
The strongly coupled D1-D5 conformal field theory is a microscopic model of black holes which is expected to have chaotic dynamics. Here, we study the weak coupling limit of the theory where it is integrable rather than chaotic. In this limit, the operators creating microstates of the lowest mass black hole are known exactly. We consider the time-ordered two-point function of light probes in these microstates, normalized by the same two-point function in vacuum. These correlators display a universal early-time decay followed by late-time sporadic behavior. To find a prescription for temporal coarse-graining of these late fluctuations we appeal to random matrix theory, where we show that a progressive time-average smooths the spectral form factor (a proxy for the 2-point function) in a typical draw of a random matrix. This coarse-grained quantity reproduces the matrix ensemble average to a good approximation. Employing this coarse-graining in the D1-D5 system, we find that the early-time decay is followed by a dip, a ramp and a plateau, in remarkable qualitative agreement with recent studies of the Sachdev-Ye-Kitaev (SYK) model. We study the timescales involved, comment on similarities and differences between our integrable model and the chaotic SYK model, and suggest ways to extend our results away from the integrable limit.