Loop-and-allied QG bibliography

[marcus]

http://arxiv.org/abs/1105.3480
Towards a Spin-foam unification of gravity, Yang-Mills interactions and matter fields
Stephon Alexander, Antonino Marciano, Ruggero Altair Tacchi
(Submitted on 17 May 2011)
"We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the broken phase of the Spin(4) symmetry. A natural 4D extension of the theory is shown. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions."
5 pages, 2 figures

http://arxiv.org/abs/1105.3703
New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D+1 = 4 spacetime dimensions. However, interesting String theories and Supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional Supergravity loop quantisations at one's disposal in order to compare these approaches. In this series of papers, we take first steps towards this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG, which does not require the time gauge and which generalises to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1,D) or SO(D+1) and the latter choice is preferred for purposes of quantisation."
28 pages

http://arxiv.org/abs/1105.3704
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our companion paper. Central to our analysis is again the appropriate treatment of the simplicity constraint. Remarkably, the simplicity constraint invariant extension of the Hamiltonian constraint, that is a necessary step in the gauge unfixing procedure, involves a correction term which is precisely the one found in the companion paper and which makes sure that the Hamiltonian constraint derived from the Palatini Lagrangian coincides with the ADM Hamiltonian constraint when Gauss and simplicity constraints are satisfied. We therefore have rederived our new connection formulation of General Relativity from an independent starting point, thus confirming the consistency of this framework."
43 pages

http://arxiv.org/abs/1105.3705
New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"We quantise the new connection formulation of D+1 General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its 'diagonal' components acting at edges of spin network functions are easily solved, its 'off-diagonal' components acting at vertices are non trivial and require a Master constraint treatment."
34 pages

http://arxiv.org/abs/1105.3706
New Variables for Classical and Quantum Gravity in all Dimensions IV. Matter Coupling
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"We employ the techniques introduced in the companion papers to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D+1 > 2 with compact gauge group. The technique that accomplishes that is similar to the one that has been introduced in 3+1 dimensions already: First one performs a canonical analysis of Lorentzian General Relativity using the time gauge and then introduces an extension of the phase space analogous to the one employed in the first paper of this series to obtain a connection theory with SO(D+1) as the internal gauge group subject to additional constraints. The success of this method rests heavily on the strong similarity of the Lorentzian and Euclidean Clifford algebras. A quantisation of the Hamiltonian constraint is provided."
13 pages

http://arxiv.org/abs/1105.3708
On the Implementation of the Canonical Quantum Simplicity Constraint
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D > 2, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary 1-1 map to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D = 3. The linear constraint operators on the other hand are non-anomalous by themselves, however their solution space will be shown to differ in D = 3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. We emphasise that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future."
22 pages, 2 figures

http://arxiv.org/abs/1105.3709
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"In our companion papers, we managed to derive a connection formulation of Lorentzian General Relativity in D+1 dimensions with compact gauge group SO(D+1) such that the connection is Poisson commuting, which implies that Loop Quantum Gravity quantisation methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature Supergravity theories, in particular 11d SUGRA and 4d, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D+1) in presence of the Rarita-Schwinger field. This is non trivial because SUSY typically requires the Rarita-Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signature. We resolve the arising tension and provide a background independent representation of the non trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature."
43 pages

http://arxiv.org/abs/1105.3710
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 18 May 2011)
"In our companion paper, we focussed on the quantisation of the Rarita-Schwinger sector of Supergravity theories in various dimensions by using an extension of Loop Quantum Gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantisation of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantisation of the 3-index photon of 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern-Simons term for the 3-index photon, which is due to local SUSY, the theory is self-interacting and its quantisation far from straightforward. Nevertheless, we show that a reduced phase space quantisation with respect to the 3-index photon Gauss constraint is possible. Specifically, the Weyl algebra of observables, which deviates from the usual CCR Weyl algebras by an interesting twist contribution proportional to the level of the Chern-Simons theory, admits a background independent state of the Narnhofer-Thirring type."
12 pages

http://arxiv.org/abs/1105.3724
Loop quantum cosmology of k=1 FRW: A tale of two bounces
Alejandro Corichi, Asieh Karami
(Submitted on 18 May 2011)
"We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially non-flat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed k=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a 'large' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the holonomy based quantum theory."
18 pages, 3 figures

Brief mention:
http://arxiv.org/abs/1105.3504
Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms
Peter Baekler (Duesseldorf), Friedrich W. Hehl (Cologne & Columbia, Missouri)
(Submitted on 17 May 2011)
Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku, and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can only be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al. and Baekler et al., emerges also in the framework of Diakonov et al.(2011). We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann-Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) Only in a Riemann-Cartan spacetime, that is, in a spacetime with torsion, parity violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann-Cartan spacetime is a natural habitat for chiral fermionic matter fields.
12 page

http://arxiv.org/abs/1105.3612
Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
Jerzy Lukierski, Mariusz Woronowicz (IFT, Wroclaw Univ.)
(Submitted on 18 May 2011)

 

[marcus]

http://arxiv.org/abs/1105.3945
Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach
Bernd J Schroers
(Submitted on 19 May 2011)
"These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants (c, G, Lambda, hbar) enter as deformation parameters. The classical situation is summarised, where solutions can be characterised in terms of model spacetimes (which depend on c and Lambda), together with global identifications via elements of the corresponding isometry groups. The quantum theory may be viewed as a deformation of this picture, with quantum groups replacing the local isometry groups, and non-commutative spacetimes replacing the classical model spacetimes. This point of view is explained, and open issues are sketched."
Talk given at Geometry and Physics in Cracow, September 2010; 22 pages, 2 figures

 

[atyy]

http://arxiv.org/abs/1105.3930
The emergence of Special and Doubly Special Relativity
Petr Jizba, Fabio Scardigli
(Submitted on 19 May 2011)
In a previous paper [Phys.Rev.D82, 085016(2010)] we introduced a method for obtaining the exact Feynman propagator of a relativistic particle (for both Klein-Gordon and Dirac case) from a superstatistical average over non-relativistic single-particle paths. We suggested that this method could offer new insights into the currently much debated issue of emergent relativity. In this paper we proceed further, showing that a Brownian motion on a short scale originates a relativistic motion on scales larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. We also present the modifications necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, an unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as generalized canonical commutation relations, connection with Feynman chessboard model, and Hausforff dimensions of corresponding path-integral trajectories are also discussed.

 

[MTd2]

http://arxiv.org/abs/1105.4194

A new look at Lorentz-Covariant Loop Quantum Gravity

Marc Geiller, Marc Lachieze-Rey, Karim Noui
(Submitted on 20 May 2011)
In this work, we study the classical and quantum properties of the Lorentz-covariant connection for loop quantum gravity found in \cite{GLNS}. The unique commutative Lorentz-covariant connection has been found by solving the second class constraints inherited from the canonical analysis of the Holst action without the time gauge. We show that this connection has the property of lying in the conjugacy class of a pure $\su(2)$ connection, a result which enables to construct the kinematical Hilbert space of the Lorentz-covariant theory in terms of the usual $\SU(2)$ spin-network states. Furthermore, we show that there is a unique Lorentz-covariant electric field, up to trivial and natural equivalence relations. The Lorentz-covariant electric field transforms under the adjoint action of the Lorentz group, and the associated Casimir operators are shown to be proportional to the area density. This gives a very interesting algebraic interpretation of the area. Finally, we show that the action of the surface operator on the Lorentz-covariant holonomies reproduces exactly the usual discrete $\SU(2)$ spectrum of time gauge loop quantum gravity. In other words, the use of the time gauge does not introduce anomalies in the quantum theory.

http://arxiv.org/abs/1105.4194

Rotation, Equivalence Principle, and GP-B Experiment

Wei-Tou Ni
(Submitted on 22 May 2011)
The ultra-precise Gravity Probe B experiment measured the frame-dragging effect and geodetic precession on four quartz gyros. We use this result to test WEP II (Weak Equivalence Principle II) which includes rotation in the universal free-fall motion. The free-fall E\"otv\"os parameter eta for rotating body is < = 10**(-11) with four-order improvement over previous results. The anomalous torque per unit angular momentum parameter lambda is constrained to (-0.05 +- 3.67) \times 10**(-15) s-1, (0.24 +- 0.98) \times 10**(-15) s-1, and (0 +- 3.6) \times 10**(-13) s-1 respectively in the directions of geodetic effect, frame-dragging effect and angular momentum axis; the dimensionless frequency-dependence parameter {\kappa} is constrained to (1.75 +- 4.96) \times 10**(-17), (1.80 +- 1.34) \times 10**(-17), and (0 +- 3) \times 10**(-14) respectively.http://arxiv.org/abs/1105.4184

Is geometry bosonic or fermionic?

Taylor L. Hughes, Andrew Randono
(Submitted on 20 May 2011)
It is generally assumed that the gravitational field is bosonic. Here we show that a simple propagating torsional theory can give rise to localized geometric structures that can consistently be quantized as fermions under exchange. To demonstrate this, we show that the model can be formally mapped onto the Skyrme model of baryons, and we use well-known results from Skyrme theory. This begs the question: {\it Is geometry bosonic or fermionic (or both)?}

 

[John86]

http://arxiv.org/abs/1105.4464
Quantum correlations with no causal order
Authors: Ognyan Oreshkov, Fabio Costa, Caslav Brukner
(Submitted on 23 May 2011)
Abstract: Much of the recent progress in understanding quantum theory has been achieved within an operational approach. Within this context quantum mechanics is viewed as a theory for making probabilistic predictions for measurement outcomes following specified preparations. However, thus far essential elements of the theory --- space, time and causal structure --- elude this operational formulation and are assumed to be fixed. Is it possible to extend the operational approach to quantum mechanics such that the notions of an underlying space-time or causal structure are not assumed? What new phenomenology can follow from such an approach? We develop a framework for multipartite quantum correlations that does not presume these notions, but simply that experimenters in their local laboratories can perform arbitrary quantum operations. All known situations that respect definite causal order, including signalling and no-signalling correlations between time-like and space-like separated experiments respectively, as well as probabilistic mixtures of these, can be expressed in this framework. Remarkably, we find situations where two experiments are neither causally ordered nor in a probabilistic mixture of definite causal orders. These correlations are shown to violate a causal inequality, enabling a communication task that is impossible if the operations are ordered according to a fixed background time. However, we show that classical correlations are always causally ordered, which suggests a deep connection between definite causal structures and classicality.

http://arxiv.org/abs/1105.4326
Testing super-deterministic hidden variables theories
Authors: Sabine Hossenfelder
(Submitted on 22 May 2011)
Abstract: We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect a super-deterministic modification of quantum mechanics to become relevant.

 

[atyy]

http://arxiv.org/abs/1105.4482
Higher Curvature Gravity and the Holographic fluid dual to flat spacetime
Goffredo Chirco, Christopher Eling, Stefano Liberati
(Submitted on 23 May 2011)
Recent works have demonstrated that one can construct a (d+2) dimensional solution of the vacuum Einstein equations that is dual to a (d+1) dimensional fluid satisfying the incompressible Navier-Stokes equations. In one important example, the fluid lives on a fixed timelike surface in the flat Rindler spacetime associated with an accelerated observer. In arXiv:1103.3022, Compere, et. al. presented an algorithm for re-constructing this solution and then used this solution to find the viscous transport coefficients for the fluid. In this paper, we show that the shear viscosity for the fluid is unchanged for a wide class of higher curvature generalizations to Einstein gravity. The choice of gravitational dynamics only affects the second order transport coefficients. We explicitly calculate these in five-dimensional Einstein-Gauss-Bonnet gravity and discuss the implications of our results.

 

[marcus]

http://arxiv.org/abs/1105.4637
Spectral Action for Robertson-Walker metrics
Ali H. Chamseddine, Alain Connes
(Submitted on 23 May 2011)
"We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a₆ against the known universal formulas of Gilkey and compute the expansion up to a₁₀ using our direct method."

 

[MTd2]

Coherent semiclassical states for loop quantum cosmology

http://arxiv.org/abs/1105.5081

Alejandro Corichi, Edison Montoya
(Submitted on 25 May 2011)
The spatially flat Friedman-Robertson-Walker (FRW) cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: i) the quantum bounce that replaces the big bang singularity is generic; ii) there is an upper bound on the energy density for all states and iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most `quantum behavior' is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the `effective theory' throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so called `cosmic forgetfulness'.

 

[MTd2]

The paper was completely rewritten and the title changed, so I will post it as it were new.

http://arxiv.org/abs/0904.1276v3

Abelian gerbes, generalized geometries and exotic R^4

Torsten Asselmeyer-Maluga, Jerzy Król
(Submitted on 8 Apr 2009 (v1), last revised 26 May 2011 (this version, v3))
In the paper we prove the existence of the strict relation between small exotic smoothness structures on the Euclidean 4-space R^4 from the radial family of De-Michellis-Freedman type, and cobordism classes of codimension one foliations of S^3. Both are distinguished by the Godbillon-Vey invariants, $GV\in H^{3}(S^{3},R)$, of the foliations which are computed from the value of radii of the radial family. The special case of integer Godbillon-Vey invariants $GV\in H^{3}(S^{3},Z)$ is also discussed and related to flat PSL(2,R)-bundles. Next we relate such distinguished small exotic smooth R^4's with twisted generalized geometries of Hitchin on TS^3+T*S^3 and abelian gerbes on S^3. In particular the change of the smoothness on R^4 corresponds to the twisting of the generalized geometry by the abelian gerbe. We formulate the localization principle for exotic 4-regions in spacetime and show that the existence of such domains causes the quantization of electric charge, the effect usually ascribed to the existence of magnetic monopoles.

 

[atyy]

http://arxiv.org/abs/1105.3122
Critical behavior of colored tensor models in the large N limit
Valentin Bonzom, Razvan Gurau, Aldo Riello, Vincent Rivasseau
Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.

 

[marcus]

http://arxiv.org/abs/1105.5582
Lattice quantum gravity - an update
J. Ambjorn, J. Jurkiewicz, R. Loll
(Submitted on 27 May 2011)
We advocate lattice methods as the tool of choice to constructively define a background-independent theory of Lorentzian quantum gravity and explore its physical properties in the Planckian regime. The formulation that arguably has most furthered our understanding of quantum gravity (and of various pitfalls present in the nonperturbative sector) uses dynamical triangulations to regularize the nonperturbative path integral over geometries. Its Lorentzian version in terms of Causal Dynamical Triangulations (CDT) - in addition to having a definite quantum signature on short scales - has been shown to reproduce important features of the classical theory on large scales. This article recaps the most important developments in CDT of the last few years for the physically relevant case of four spacetime dimensions, and describes its status quo at present.
14 pages, 8 figures, write-up of plenary talk at Lattice 2010, Villasimius, Sardegna, Italy, 14-19 June 2010


Brief mention (not QG but result may possibly be useful or of general interest):
http://arxiv.org/abs/1105.5632
Einstein Gravity from Conformal Gravity
Juan Maldacena
(Submitted on 27 May 2011)
We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation.
In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, |Psi[g]|², for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.
26 pages, 1 figure,

 

[MTd2]

http://arxiv.org/abs/1105.5646

Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations

Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner
(Submitted on 27 May 2011)
We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can fully reproduce the behaviour of the latter in this regime. In particular, we show that Horava-Lifgarbagez gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to indicate that the two theories lie in the same universality class.

http://arxiv.org/abs/1105.6034

Black hole state counting in loop quantum gravity

A. Ghosh, P. Mitra
(Submitted on 26 May 2011)
The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.

 

[marcus]

http://arxiv.org/abs/1105.5687
Gravity as an emergent phenomenon: a GFT perspective
Lorenzo Sindoni
(Submitted on 28 May 2011)
While the idea of gravity as an emergent phenomenon is an intriguing one, little is known about concrete implementations that could lead to viable phenomenology, most of the obstructions being related to the intrinsic difficulties of formulating genuinely pregeometric theories. In this paper we present a preliminary discussion of the impact of critical behavior of certain microscopic models for gravity, based on group field theories, on the dynamics of the macroscopic regime. The continuum limit is examined in light of some scaling assumption, and the relevant consequences for low energy effective theories are discussed, the role of universality, the corrections to scaling, the emergence of gravitational theories and the nature of their thermodynamical behavior.
27 pages

http://arxiv.org/abs/1105.6036
Discrete Symmetry in the EPRL Model and Neutrino Physics
Louis Crane
(Submitted on 30 May 2011)
In ref. [1], we proposed a new interpretation of the EPRL quantization of the BC model for quantum general relativity using a monoidal functor we call the time functor. In this preliminary draft we apply the theory of modules over monoidal functors [2] to the time functor, to propose an extension of the EPRL model which would include the standard model. This is motivated by recent advances in neutrino Physics.
11 pages

 

[MTd2]

ALMOST UNNOTICED, VERY IMPORTANT:

http://arxiv.org/abs/1105.6072v1

A generalization of the Virasoro algebra to arbitrary dimensions

Razvan Gurau
(Submitted on 30 May 2011)
Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimensions.

 

[marcus]

http://arxiv.org/abs/1105.6098
From dispersion relations to spectral dimension - and back again
Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner
(Submitted on 30 May 2011)
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical triangulations (CDT) and Horava gravity as possible candidates for quantum gravity. We advocate the use of the spectral dimension as a probe for the kinematics of these (and other) systems in the region where spacetime curvature is small, and the manifold is flat to a good approximation. In particular, we show how to assign a spectral dimension (as a function of so-called diffusion time) to any arbitrarily specified dispersion relation. We also analyze the fundamental properties of spectral dimension using extensions of the usual Seeley-DeWitt and Feynman expansions, and by saddle point techniques. The spectral dimension turns out to be a useful, robust and powerful probe, not only of geometry, but also of kinematics.
26 pages

http://arxiv.org/abs/1105.6234
Quantum Gravity phenomenology: achievements and challenges
Stefano Liberati (SISSA, Trieste and INFN, Trieste), Luca Maccione (DESY, Hamburg)
(Submitted on 31 May 2011)
Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by O(E²/M_Pl²) and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks.
Proceedings of ERE2010

 

[marcus]

http://arxiv.org/abs/1106.0295
Discrete to continuum transition in multifractal spacetimes
Gianluca Calcagni
(Submitted on 1 Jun 2011)
We outline a proposal for a multifractal spacetime whose properties are dictated by general arguments from fractal geometry. There exists a fine hierarchy of scales identifying different regimes, from an ultramicroscopic fractal structure to a sequence of continuum phases where discrete symmetries progressively melt in a continuum. Geometric information is encoded in the symmetry and harmonic structure of the spacetime measure. The measure is characterized by a scale-dependent Hausdorff dimension and by logarithmic oscillations governed by a fundamental length. Consequences for noncommutative field theories and discrete quantum-gravity approaches are discussed.
4 pages

http://arxiv.org/abs/1106.0126
Hořava-Lifgarbagez Quantum Cosmology
Orfeu Bertolami, Carlos A. D. Zarro
(Submitted on 1 Jun 2011)
In this work, a minisuperspace model for the projectable Hořava-Lifgarbagez (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to HL gravity, there is a "potential barrier" nearby a=0. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the GR behaviour for the late universe.
27 pages, 7 figures

 

[marcus]

http://arxiv.org/abs/1106.0313
Relative locality: A deepening of the relativity principle
Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin
(Submitted on 1 Jun 2011)
We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which hbar and G_N may be neglected, while their ratio, the Planck mass M_p = sqrt[hbar/G_N], is important. We propose that M_p governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.
8 pages, this essay was awarded Second Prize in the 2011 Essay Competition of the Gravity Research Foundation

 

[MTd2]

http://arxiv.org/abs/1106.0261

Minimal length in quantum space and integrations of the line element in Noncommutative Geometry

Pierre Martinetti, Flavio Mercati, Luca Tomassini
(Submitted on 1 Jun 2011)
We question the emergence of a minimal length in quantum spacetime, confronting two notions that appeared at various points in the literature: length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime and the canonical noncommutative spacetime (theta-Minkowski) on the one side; Connes spectral distance in noncommutative geometry on the other side. Although on the Euclidean space - as well as on manifolds with suitable symmetry - the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular, the widespread idea that quantizing the coordinates inevitably yields a minimal length should be handle with care: on the Moyal plane for instance, both the quantum length (intended as the mean value of the length operator on a separable two-point state) and the spectral distance are discrete, but only the former is bounded above from zero. We propose a framework in which the comparison of the two objects makes sense: by doubling the spectral triple, one turns the quantum length into a true distance function and, simultaneously, emphasises the "quantum mechanics flavor" of the spectral distance. Specifically, for any couple of identical states, the quantum length is identified with the spectral distance on a two-sheet model (each state living on a distinct sheet). Using Pythagoras-like relations for spectral triples, we extend the identification to any couples of distinct states, provided the spectral distance on a single sheet coincides with a new distance induced by the length operator. This condition is not fulfilled on the Moyal plane. We interpret this discrepancy (which becomes negligible at high energy) as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane.

 

[marcus]

http://arxiv.org/abs/1106.1103
Towards Loop Quantum Supergravity (LQSG)
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
(Submitted on 6 Jun 2011)
Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11 dimensions. String Theory is a top to bottom approach to Quantum Supergravity in that it postulates a new object, the string, from which classical supergravity emerges as a low energy limit. On the other hand, one may try more traditional bottom to top routes and apply the techniques of Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background independent and non perturbative approach to the quantisation of classical General Relativity, however, so far mostly without supersymmetry. The main obstacle to the extension of the techniques of LQG to the quantisation of higher dimensional Supergravity is that LQG rests on a specific connection formulation of General Relativity which exists only in D + 1 = 4 dimensions. In this paper we introduce a new connection formulation of General Relativity which exists in all spacetime dimensions. We show that all LQG techniques developed in D + 1 = 4 can be transferred to the new variables in all dimensions and describe how they can be generalised to the new types of fields that appear in Supergravity Theories as compared to standard matter, specifically Rarita-Schwinger and p-form gauge fields.
12 pages

Brief mention of papers of possible relevance to Loop-and-allied QG or of general interest:
http://arxiv.org/abs/1106.1118
Gravitational collapse of quantum matter
Benjamin K. Tippett, Viqar Husain
(Submitted on 6 Jun 2011)
We describe a class of exactly soluble models for gravitational collapse in spherical symmetry obtained by patching dynamical spherically symmetric exterior spacetimes with cosmological interior spacetimes...
8 pages, 4 figures

http://arxiv.org/abs/1106.0920
Background-Independence
Gordon Belot
(Submitted on 5 Jun 2011)
Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion...

http://arxiv.org/abs/1106.0767
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Murray Gell-Mann, James B. Hartle
(Submitted on 3 Jun 2011)
Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one...
...We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.
11 pages, one figure

http://arxiv.org/abs/1106.0748
Restoring Local Causality and Objective Reality to the Entangled Photons
Joy Christian (Oxford)
(Submitted on 3 Jun 2011)
Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. This well known fact was brought forth by Einstein, Podolsky, and Rosen (EPR) in 1935. Today it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell's theorem and its supporting experiments. By contrast, we provide a strictly local, deterministic, and realistic explanation for the correlations observed in two such supporting experiments performed at Orsay and Innsbruck...
8 pages; Forthcoming in a FQXi sponsored book on Bell's Theorem and Quantum Entanglement (2011)

 

[marcus]

http://arxiv.org/abs/1106.1417
Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?
Rodolfo Gambini, Saeed Rastgoo, Jorge Pullin
(Submitted on 7 Jun 2011)
We discuss the applicability of the argument of Collins, Pérez, Sudarsky, Urrutia and Vucetich to loop quantum gravity. This argument suggests that Lorentz violations, even ones that only manifest themselves at energies close to the Planck scale, have significant observational consequences at low energies when one considers perturbative quantum field theory and renormalization. We show that non-perturbative treatments like those of loop quantum gravity may generate deviations of Lorentz invariance of a different type than those considered by Collins et al. that do not necessarily imply observational consequences at low energy.
9 pages, 1 figure, to appear in Class. Quan. Grav

Brief mention:
http://arxiv.org/abs/1106.1302
Dirac Equation in the Magueijo-Smolin Approach of Double Special Relativity
Z. Belhadi, F. Ménas, A. Bérard, P. Gosselin, H. Mohrbach
(Submitted on 7 Jun 2011)
We reconsider in details the Dirac equation in the context of the Magueijo-Smolin approach to the Doubly Special Relativity. Starting from the deformed dispersion relation we obtain the Dirac equation in momentum space, allowing us to achieve a more in-depth study of its semiclassical approach. Finally by means of a deformed correspondence principle we gain access to an equation in the position space.

http://arxiv.org/abs/1106.1198
Finally, results from Gravity Probe-B
Clifford M. Will
(Submitted on 6 Jun 2011)
Nearly fifty years after its inception, the Gravity Probe B satellite mission delivers the first measurements of how a spinning gyroscope precesses in the gravitational warping of spacetime.

 

[marcus]

http://arxiv.org/abs/1106.1448
Towards Loop Quantization of Plane Gravitational Waves
Franz Hinterleitner, Seth Major
(Submitted on 7 Jun 2011)
The polarized Gowdy model in terms of Ashtekar-Barbero variables is further reduced by including the Killing equations for plane-fronted parallel gravitational waves with parallel rays. The resulting constraint algebra, including one constraint derived from the Killing equations in addition to the standard ones of General Relativity, are shown to form a set of first-class constraints. Using earlier work by Banerjee and Date the constraints are expressed in terms of classical quantities that have an operator equivalent in Loop Quantum Gravity, making space-times with pp-waves accessible to loop quantization techniques.
14 pages

 

[MTd2]

http://arxiv.org/abs/1106.1460

A local induced action for the noncritical string

W. Westra, S. Zohren
(Submitted on 7 Jun 2011)
We present an alternative to Polyakov's induced action for the noncritical string. Our induced action is both local and invariant under coordinate transformations. The effective action is of Liouville type in the conformal gauge while, remarkably, in the proper-time gauge it gives the effective action of the Causal Dynamical Triangulation (CDT) approach to 2d quantum gravity. In the latter gauge the effective action is especially interesting since its quantization simply reduces to a quantum mechanical model.

http://arxiv.org/abs/1106.1435

From Asymptotic Safety to Dark Energy

Changrim Ahn, Chanju Kim, Eric V. Linder
(Submitted on 7 Jun 2011)
We consider renormalization group flow applied to the cosmological dynamical equations. A consistency condition arising from energy-momentum conservation links the flow parameters to the cosmological evolution, restricting possible behaviors. Three classes of cosmological fixed points for dark energy plus a barotropic fluid are found: a dark energy dominated universe, which can be either accelerating or decelerating depending on the RG flow parameters, a barotropic dominated universe where dark energy fades away, and solutions where the gravitational and potential couplings cease to flow. If the IR fixed point coincides with the asymptotically safe UV fixed point then the dark energy pressure vanishes in the first class, while (only) in the de Sitter limit of the third class the RG cutoff scale becomes the Hubble scale.

 

[atyy]

http://arxiv.org/abs/1106.1082
Tensor network states and geometry
G. Evenbly, G. Vidal
(Submitted on 6 Jun 2011)
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law -- that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.

 

[john baez]

The abstract of the new Sotiriou-Visser-Weinfurtner paper sounds pretty explosive:

We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can fully reproduce the behaviour of the latter in this regime. In particular, we show that Hořava-Lifgarbagez gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to indicate that the two theories lie in the same universality class.

Because causal dynamical triangulations slices up spacetime into surfaces of "constant time", I'd always worried that it was quantizing not general relativity but some other theory - one that has a built-in separation between time and space. Hořava-Lifgarbagez gravity is such a theory. Wikipedia writes:

Hořava-Lifgarbagez gravity (or Hořava gravity) is a theory of quantum gravity proposed by Petr Hořava in 2009. It solves the problem of different concepts of time in quantum field theory and general relativity by treating the quantum concept as the more fundamental so that space and time are not equivalent (anisotropic). The relativistic concept of time with its Lorentz invariance emerges at large distances. The theory relies on the theory of foliations to produce its causal structure. It is related to topologically massive gravity and the Cotton tensor. It is a possible UV completion of general relativity. The novelty of this approach, compared to previous approaches to quantum gravity such as Loop quantum gravity, is that it uses concepts from condensed matter physics such as quantum critical phenomena. Hořava's initial formulation was found to have side-effects such as predicting very different results for a spherical Sun compared to a slightly non-spherical Sun, so others have modified the theory. Inconsistencies remain.

How are the causal dynamical triangulations people reacting to the work of Sotiriou, Visser, and Weinfurtner? Do they agree that they may be quantizing Hořava-Lifgarbagez gravity?

I haven't been paying attention to this stuff, but I may find out the answer to this question when I go to http://www.conferences.itp.phys.ethz.ch/doku.php?id=qg11:start".

By the way, your posts listing these abstracts serve as a nice quick way to catch up on recent work in quantum gravity. Thanks! I don't want to seem like I'm completely out of the loop.

 

[john baez]

Hmm, here's what Ambjorn and Loll say in their http://arxiv.org/abs/1105.5582" :

What is curious about the phase structure of four-dimensional CDT quantum gravity is its resemblance with that of Horava-Lifgarbagez gravity [17], which has been spelled out further in [18,19]. It gives rise to the intriguing conjecture that there may be a universal phase diagram governing systems of higher-dimensional, dynamical geometry, and accomodating a variety of gravity theories, some of which may be anisotropic in space and time.

To someone raised on relativity it would seem a painful step to admit one is quantizing a theory where there really is a single "right" notion of time, and Lorentz transformations are just a kind of approximate symmetry, good at macroscopic scales. Maybe they hope they can get at quantum general relativity as one point in the phase diagram of Horava-Lifgarbagez theories.

 

[MTd2]

John Baez, this is a thread for archiving mostly papers of non-stringy gravity theories. So, because of this, I opened a thread for your comments:

https://www.physicsforums.com/showthread.php?p=3352794#post3352794

 

[marcus]

MTd2, thanks for starting a separate thread to discuss points JB just raised. I fixed one of his links from a few posts back, that contained a typo:

...
I haven't been paying attention to this stuff, but I may find out the answer to this question when I go to http://www.conferences.itp.phys.ethz.ch/doku.php?id=qg11:start".

By the way, your posts listing these abstracts serve as a nice quick way to catch up on recent work in quantum gravity. Thanks! I don't want to seem like I'm completely out of the loop.

I expect we are both pleased that our bibliography thread has been of use to him. It's nice to get some feedback!

 

[atyy]

http://arxiv.org/abs/1106.1847
Ward-Takahashi identities for the colored Boulatov model
Joseph Ben Geloun
(Submitted on 9 Jun 2011)
Ward-Takahashi identities of the colored Boulatov model are derived using a generic unitary field transformation. In a specific instance, this generic transformation turns out to be a symmetry of the interaction so that particular classes of reduced Ward-Takahashi identities for that symmetry are consequently identified.

 

[marcus]

http://arxiv.org/abs/1106.2131
Hamiltonian structure of Horava gravity
William Donnelly, Ted Jacobson
(Submitted on 10 Jun 2011)
The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second class, except for a global, first-class part that generates time reparameterizations. A reduced phase space formulation is given in which the local part of the scalar constraint is solved formally for the lapse as a function of the 3-metric and its conjugate momentum. In the infrared limit the scalar constraint is linear in the square root of the lapse. For asymptotically flat boundary conditions the Hamiltonian is a sum of bulk constraints plus a boundary term that gives the total energy. This energy expression is identical to the one for Einstein-aether theory which, for static spherically symmetric solutions, is the usual ADM energy of general relativity with a rescaled Newton constant.
8 pages,

 

[ensabah6]

http://arxiv.org/abs/1106.2121

A Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills Framework
Jong-Ping Hsu
(Submitted on 10 Jun 2011)

Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators $T_{\mu}(=\p/\p x^{\mu})$ do not have constant matrix representations. By gauging $T(4) \times SU(2) \times U(1)$ in flat space-time, we have a new tensor field $\phi_{\mu\nu}$ which universally couples to all particles and anti-particles with the same constant $g$, which has the dimension of length. In this unified model, the T(4) gauge symmetry dictates that all wave equations of fermions, massive bosons and the photon in flat space-time reduce to a Hamilton-Jacobi equation with the same `effective Riemann metric tensor' in the geometric-optics limit. Consequently, the results are consistent with experiments. We demonstrated that the T(4) gravitational gauge field can be quantized in inertial frames.

Comments: 12 pages. To be published in "Modern Physics Letters A"
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Cite as: arXiv:1106.2121v1 [hep-th]