# Our picks for first quarter 2015 MIP (most important QG paper)

## Which paper(s) will contribute most significantly to future research?

1. Apr 2, 2015

### marcus

Indicate the papers you think will prove most significant for future Loop-and-allied QG research. The poll is multiple choice, so it's possible to vote for several. Abstracts follow in the next post. With one exception, the papers are listed chronologically: latest first. The exception was a very recent paper that was spotted by John86, and added at the end.

http://arxiv.org/abs/1503.09154
Some implications of signature-change in cosmological models of loop quantum gravity
Martin Bojowald, Jakub Mielczarek

http://arxiv.org/abs/1503.07855
Loop quantum cosmology with self-dual variables
Edward Wilson-Ewing

http://arxiv.org/abs/1503.06472
Black holes in Asymptotically Safe Gravity
Frank Saueressig, Natalia Alkofer, Giulio D'Odorico, Francesca Vidotto

http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip

http://arxiv.org/abs/1502.06770
Quantum Transitions Between Classical Histories: Bouncing Cosmologies
James Hartle, Thomas Hertog

http://arxiv.org/abs/1502.06125
ΛCDM Bounce Cosmology without ΛCDM: the case of modified gravity
S.D. Odintsov, V.K. Oikonomou

http://arxiv.org/abs/1502.04640
The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
Jonathan Engle, Antonia Zipfel

http://arxiv.org/abs/1502.03410
The Montevideo Interpretation of Quantum Mechanics: a short review
Rodolfo Gambini, Jorge Pullin

http://arxiv.org/abs/1502.00278
Compact phase space, cosmological constant, discrete time
Carlo Rovelli, Francesca Vidotto

http://arxiv.org/abs/1501.06270
Matter Bounce Scenario in F(T) gravity
Jaume Haro, Jaume Amorós

http://arxiv.org/abs/1501.03007
The shape dynamics description of gravity
Tim Koslowski

http://arxiv.org/abs/1501.02963
Quantum Geometry and Black Holes
J. Fernando Barbero G., Alejandro Perez

http://arxiv.org/abs/1501.00855
Closure constraints for hyperbolic tetrahedra
Christoph Charles, Etera R. Livine

http://arxiv.org/abs/1503.08725
Statistical mechanics of reparametrization invariant systems. Takes Three to Tango
Thibaut Josset, Goffredo Chirco, Carlo Rovelli

Last edited: Apr 2, 2015
2. Apr 2, 2015

### marcus

http://arxiv.org/abs/1503.09154
Some implications of signature-change in cosmological models of loop quantum gravity
Martin Bojowald, Jakub Mielczarek
(Submitted on 31 Mar 2015)
Signature change at high density has been obtained as a possible consequence of deformed space-time structures in models of loop quantum gravity. This article provides a conceptual discussion of implications for cosmological scenarios, based on an application of mathematical results for mixed-type partial differential equations (the Tricomi problem). While the effective equations from which signature change has been derived are shown to be locally regular and therefore reliable, the underlying theory of loop quantum gravity may face several global problems in its semiclassical solutions.
35 pages, 5 figures

http://arxiv.org/abs/1503.07855
Loop quantum cosmology with self-dual variables
Edward Wilson-Ewing
(Submitted on 26 Mar 2015)
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular measure for the inner product in the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators, some of which are well-defined; these operators in turn are used in the definition of a Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum dynamics are similar, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
10 pages http://inspirehep.net/record/1356275

http://arxiv.org/abs/1503.06472
Black holes in Asymptotically Safe Gravity
Frank Saueressig, Natalia Alkofer, Giulio D'Odorico, Francesca Vidotto
(Submitted on 22 Mar 2015)
Black holes are among the most fascinating objects populating our universe. Their characteristic features, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. In this note we observe that the renormalization group improved Schwarzschild black holes constructed by Bonanno and Reuter within Weinberg's asymptotic safety program constitute a prototypical example of a Hayward geometry used to model non-singular black holes within quantum gravity phenomenology. Moreover, they share many features of a Planck star: their effective geometry naturally incorporates the one-loop corrections found in the effective field theory framework, their Kretschmann scalar is bounded, and the black hole singularity is replaced by a regular de Sitter patch. The role of the cosmological constant in the renormalization group improvement process is briefly discussed.
6 pages, 3 figures; prepared for the proceedings of the conference "Frontiers of Fundamental Physics 14"

http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015)
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
8 pages

http://arxiv.org/abs/1502.06770
Quantum Transitions Between Classical Histories: Bouncing Cosmologies
James Hartle, Thomas Hertog
(Submitted on 24 Feb 2015)
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications:
(a) Classical histories are generally available only in limited patches of the configuration space on which the state lives.
(b) In a given patch states generally predict relative probabilities for an ensemble of possible classical histories.
(c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches.
(d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion.
We support and illustrate (a)-(d) by calculating the quantum transition across the de Sitter like throat connecting asymptotically classical, inflating histories in the no-boundary quantum state. This supplies probabilities for how a classical history on one side transitions and branches into a range of classical histories on the opposite side. We also comment on the implications of (a)-(d) for the dynamics of black holes and eternal inflation.
36 pages, 6 figures

http://arxiv.org/abs/1502.06125
ΛCDM Bounce Cosmology without ΛCDM: the case of modified gravity
S.D. Odintsov, V.K. Oikonomou
(Submitted on 21 Feb 2015)
We provide an F(R) gravity description of a ΛCDM bouncing model, without the need for matter fluids or for cosmological constant. As we explicitly demonstrate, the two cosmological eras that constitute the ΛCDM bouncing model, can be generated by F(R) gravity which can lead to accelerating cosmologies. The resulting F(R) gravity has Einstein frame inflationary properties that have concordance to the latest Planck observational data. Both the F(R) gravity stability properties are thoroughly investigated and also, the gravitational particle production, a feature necessary for the viability of the ΛCDM bounce scenario, is also addressed. As we will show, the ΛCDM bounce model can be successfully described by pure F(R) gravity, with appealing phenomenological attributes, which we extensively discuss.
31 pages, accepted by PRD

http://arxiv.org/abs/1502.04640
The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
Jonathan Engle, Antonia Zipfel
(Submitted on 16 Feb 2015)
Spin foam models, an approach to defining the dynamics of loop quantum gravity, make use of the Plebanski formulation of gravity, in which gravity is recovered from a topological field theory via certain constraints called simplicity constraints. However, the simplicity constraints in their usual form select more than just one gravitational sector as well as a degenerate sector. This was shown, in previous work, to be the reason for the "extra" terms appearing in the semiclassical limit of the Euclidean EPRL amplitude. In this previous work, a way to eliminate the extra sectors, and hence terms, was developed, leading to the what was called the Euclidean proper vertex amplitude. In the present work, these results are extended to the Lorentzian signature, establishing what is called the Lorentzian proper vertex amplitude. This extension is non-trivial and involves a number of new elements since, for Lorentzian bivectors, the split into self-dual and anti-self-dual parts, on which the Euclidean derivation was based, is no longer available. In fact, the classical parts of the present derivation provide not only an extension to the Lorentzian case, but also, with minor modifications, provide a new, more four dimensionally covariant derivation for the Euclidean case. The new elements in the quantum part of the derivation are due to the different structure of unitary representations of the Lorentz group.
36 pages

http://arxiv.org/abs/1502.03410
The Montevideo Interpretation of Quantum Mechanics: a short review
Rodolfo Gambini, Jorge Pullin
(Submitted on 11 Feb 2015)
The Montevideo interpretation of quantum mechanics, which consists in supplementing environmental decoherence with fundamental limitations in measurement stemming from gravity, has been described in several publications. However, some of them appeared before the full picture provided by the interpretation was developed. As such it can be difficult to get a good understanding via the published literature. Here we summarize it in a self contained brief presentation including all its principal elements.
10 pages

http://arxiv.org/abs/1502.00278
Compact phase space, cosmological constant, discrete time
Carlo Rovelli, Francesca Vidotto
(Submitted on 1 Feb 2015)
We study the quantization of geometry in the presence of a cosmological constant, using a discretization with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
6 pages

http://arxiv.org/abs/1501.06270
Matter Bounce Scenario in F(T) gravity
Jaume Haro, Jaume Amorós
(Submitted on 26 Jan 2015)
It is shown that teleparallel F(T) theories of gravity combined with holonomy corrected Loop Quantum Cosmology (LQC) support a Matter Bounce Scenario (MBS) which is a potential alternative to the inflationary paradigm. The Matter Bounce Scenario is reviewed and, according to the current observational data provided by PLANCK's team, we have summarized all the conditions that it has to satisfy in order to be a viable alternative to inflation, such as to provide a theoretical value of the spectral index and its running compatible with the latest PLANCK data, to have a reheating process via gravitational particle production, or to predict some signatures in the non-gaussianities of the power spectrum. The calculation of the power spectrum for scalar perturbations and the ratio of tensor to scalar perturbations has been done, in the simplest case of an exact matter dominated background, for both holonomy corrected LQC and teleparallel F(T) gravity. Finally, we have discussed the challenges (essentially, dealing with non-gaussianities, the calculation of the 3-point function in flat spatial geometries for theories beyond General Relativity) and problems (Jeans instabilities in the case of holonomy corrected LQC or local Lorentz dependence in teleparallelism) that arise in either bouncing scenario.
6 pages. Communication to the FFP2014 (Frontiers in Fundamental Physics, Marseille 2014). To appear in Proceedings of Science

http://arxiv.org/abs/1501.03007
The shape dynamics description of gravity
Tim Koslowski
(Submitted on 13 Jan 2015)
Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than GR) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of spacetime in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of spacetime geometry, the role of local Minkowski space, universality of spacetime geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincare group. In this contribution I derive effective spacetime structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an "experienced spacetime geometry." This leads (in an idealized approximation) to local Minkowski space and causal relations. The small scale structure of the emergent geometric picture depends on the specific probes used to experience spacetime, which limits the applicability of effective spacetime to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski spacetime emerges from the evolution of quantum particles.
16 pages, a submission to the proceedings of Theory Canada 9

http://arxiv.org/abs/1501.02963
Quantum Geometry and Black Holes
J. Fernando Barbero G., Alejandro Perez
(Submitted on 13 Jan 2015)
We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity. After an introduction that discusses the main conceptual issues we present some details about the classical and quantum geometry of isolated horizons and their quantum geometry and then use this scheme to give a natural definition of the entropy of black holes. The entropy computations can be neatly expressed in the form of combinatorial problems solvable with the help of methods based on number theory and the use of generating functions. The recovery of the Bekenstein-Hawking law and corrections to it is explained in some detail. After this, due attention is paid to the discussion of semiclassical issues. An important point in this respect is the proper interpretation of the horizon area as the energy that should appear in the statistical-mechanical treatment of the black hole model presented here. The chapter ends with a comparison between the microscopic and semiclassical approaches to the computation of the entropy and discusses a number of issues regarding the relation between entanglement and statistical entropy and the possibility of comparing the subdominant (logarithmic) corrections to the entropy obtained with the help of the Euclidean path integral with the ones obtained in the present framework.
39 pages. Contribution to appear in the World Scientific series "100 Years of General Relativity" edited by A. Ashtekar and J. Pullin

http://arxiv.org/abs/1501.00855
Closure constraints for hyperbolic tetrahedra
Christoph Charles, Etera R. Livine
(Submitted on 5 Jan 2015)
We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its classical states are graphs provided with algebraic data. In particular closure constraints at every node of the graph ensure their interpretation as twisted geometries. Dual to each node, one has a polyhedron embedded in flat space R3. One then glues them allowing for both curvature and torsion. It was recently conjectured that q-deforming the gauge group SU(2) would allow to account for a non-vanishing cosmological constant Lambda, and in particular that deforming the loop gravity phase space with real parameter q>0 would lead to a generalization of twisted geometries to a hyperbolic curvature. Following this insight, we look for generalization of the closure constraints to the hyperbolic case. In particular, we introduce two new closure constraints for hyperbolic tetrahedra. One is compact and expressed in terms of normal rotations (group elements in SU(2) associated to the triangles) and the second is non-compact and expressed in terms of triangular matrices (group elements in SB(2,C)). We show that these closure constraints both define a unique dual tetrahedron (up to global translations on the three-dimensional one-sheet hyperboloid) and are thus ultimately equivalent.
24 pages

http://arxiv.org/abs/1503.08725
Statistical mechanics of reparametrization invariant systems. Takes Three to Tango
Thibaut Josset, Goffredo Chirco, Carlo Rovelli
(Submitted on 30 Mar 2015)
It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics. We focus on reparametrization invariant systems without additional gauges. The key idea is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non-interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components ---roughly: a clock and two systems among which a generalization of energy is equi-partitioned. The key property that allows the application of statistical mechanics and thermodynamics is an additivity condition of such generalized energy.
9 pages, 2 figures

Last edited: Apr 2, 2015
3. Jun 9, 2015

### marcus

Time to start gathering and sorting candidate papers for the 2nd quarter MIP poll:
http://arxiv.org/abs/1504.01065
Wilson loops in CDT quantum gravity
J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll
(Submitted on 4 Apr 2015)
By explicit construction, we show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We use this set-up to investigate a class of Wilson line observables associated with the world line of a point particle coupled to quantum gravity, and deduce from their expectation values that the underlying holonomies cover the group manifold of SO(4) uniformly.
30 pages, 5 figures

http://arxiv.org/abs/1504.02068
Hamiltonian operator for loop quantum gravity coupled to a scalar field
E. Alesci, M. Assanioussi, J. Lewandowski, I. Mäkinen
(Submitted on 8 Apr 2015)
We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on the idea of so-called "special loops". We discuss in detail the regularization procedure and the assignment of the loops, along with the properties of the resulting operator. We compute the action of the squared Hamiltonian operator on spin network states, and close with some comments and outlooks.
31 pages, numerous graph diagrams

http://arxiv.org/abs/1504.02169
Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework, and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g. spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article, and its companion, affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

http://arxiv.org/abs/1504.02170
Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G=U(1)n and support by numerical evidence for G=SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation, that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask, whether a similar connection exists for compact Lie groups, as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.

http://arxiv.org/abs/1504.02171
Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.

http://arxiv.org/abs/1504.02822
Duality between Spin networks and the 2D Ising model
Valentin Bonzom, Francesco Costantino, Etera R. Livine
(Submitted on 11 Apr 2015)
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories which couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
35 pages

http://arxiv.org/abs/1504.05352
Black hole spectroscopy from Loop Quantum Gravity models
Aurelien Barrau, Xiangyu Cao, Karim Noui, Alejandro Perez
(Submitted on 21 Apr 2015)
Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter γ. Starting with black holes of initial horizon area A∼102 in Planck units, we present the spectra for different values of γ. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that γ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.
11 pages, 9 figures

http://arxiv.org/abs/1504.07559
Loop quantum cosmology: From pre-inflationary dynamics to observations
Abhay Ashtekar, Aurelien Barrau
(Submitted on 28 Apr 2015)
The Planck collaboration has provided us rich information about the early universe, and a host of new observational missions will soon shed further light on the anomalies' that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.
20 pages, 5 figures. Invited review article for the "focus issue" of Classical and Quantum Gravity : "Planck and the fundamentals of cosmology"

http://arxiv.org/abs/1504.07100
Quantum Holonomy Theory
Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 27 Apr 2015)
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit.
76 pages, 6 figures

http://arxiv.org/abs/1505.00223
Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator
Jinsong Yang, Yongge Ma
(Submitted on 1 May 2015)
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In the series of papers, we will introduce a graphical method, developed by Yutsis and Brink, to loop quantum gravity. The graphical method provides a very powerful technique for simplifying complicated calculations. In this first paper, the closed formula of volume operator is derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the acting of operators as well as the spin network states, we use the simple rules for transforming graphs to yield the resulting formula. Comparing with the complicated algebraic derivation in some literatures, our procedure is more concise, intuitive and visual. The resulting matrix elements of volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin network states.
40 pages

http://arxiv.org/abs/1505.00225
Graphical method in loop quantum gravity: II. The Hamiltonian constraint and inverse volume operators
Jinsong Yang, Yongge Ma
(Submitted on 1 May 2015)
This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Hamiltonian constraint operator and the so-called inverse volume operator on spin network states with trivalent vertices. Both of the operators involve the co-triad operator which contains holonomies by construction. The non-ambiguous, concise and visual characters of our graphical method ensure the rigour for our calculations. Our results indicate some corrections to the existing results in literatures for both operators.
19 pages

http://arxiv.org/abs/1505.03119
Computing the Effective Action with the Functional Renormalization Group
Alessandro Codello, Roberto Percacci, Leslaw Rachwal, Alberto Tonero
(Submitted on 12 May 2015)
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action Γk. The ordinary effective action Γ0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We use the results of Barvinsky, Vilkovisky and Avramidi on the non-local heat kernel coefficients to reproduce the four point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
40 pages

http://arxiv.org/abs/1505.04088
Gravitational crystal inside the black hole
H. Nikolic
(Submitted on 15 May 2015)
Crystals, as quantum objects typically much larger than their lattice spacing, are a counterexample to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black-hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.
6 pages

http://arxiv.org/abs/1505.04753
Entanglement equilibrium and the Einstein equation
Ted Jacobson
(Submitted on 18 May 2015)
We show that the semiclassical Einstein equation holds if and only if the entanglement entropy in small causal diamonds is stationary at constant volume, when varied from a maximally symmetric vacuum state of geometry and quantum fields. The argument hinges on a conjecture about the variation of the conformal boost energy of quantum fields in small diamonds.
7 pages

http://arxiv.org/abs/1506.00299
New scalar constraint operator for loop quantum gravity
Mehdi Assanioussi, Jerzy Lewandowski, Ilkka Mäkinen
(Submitted on 31 May 2015)
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of these operators on a general level.
14 pages.

http://arxiv.org/abs/1506.00927
The strange equation of quantum gravity
Carlo Rovelli
(Submitted on 2 Jun 2015)
Disavowed by one its fathers, ill defined, never empirically tested, the Wheeler-DeWitt equation has nevertheless had a powerful influence on fundamental physics. A well deserved one.
7 pages. Appeared in the Classical and Quantum Gravity Focus issue: Milestones of general relativity.

http://arxiv.org/abs/1506.01018
Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole
Shohreh Abdolrahimi, Don N. Page
(Submitted on 2 Jun 2015)
Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.
17 pages.

http://arxiv.org/abs/1506.03053
Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
Hal M. Haggard, Muxin Han, Aldo Riello
(Submitted on 9 Jun 2015)
We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces. Euclidean notions such as the normal vector to a face are replaced by Levi-Civita holonomies around each of the tetrahedron's faces. This allows the reconstruction of both spherical and hyperbolic tetrahedra within a unified framework. A new type of hyperbolic simplex is introduced in order for all the sectors encoded in the algebraic data to be covered. Generalizing the phase space of shapes associated to flat tetrahedra leads to group valued moment maps and quasi-Poisson spaces. These discrete geometries provide a natural arena for considering the quantization of gravity including a cosmological constant. A concrete realization of this is provided by the relation with the spin-network states of loop quantum gravity. This work therefore provides a bottom-up justification for the emergence of deformed gauge symmetries and quantum groups in 3+1 dimensional covariant loop quantum gravity in the presence of a cosmological constant.
38 pages and 9 figures

http://arxiv.org/abs/1506.02965
Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
Georgios Kofinas, Vasilios Zarikas
(Submitted on 9 Jun 2015)
New general spherically symmetric solutions have been derived with a cosmological "constant" Λ as a source. This Λ field is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.
15 pages

Last edited: Jun 11, 2015
4. Jun 9, 2015

### marcus

http://arxiv.org/abs/1506.02938
Quantum mechanics and the principle of maximal variety
Lee Smolin
(Submitted on 9 Jun 2015)
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem.
The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation.
The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically.
This proposal could be tested by constructing quantum devices from entangled states of a modest number of qubits which, by its combinatorial complexity, can be expected to have no natural copies.
24 pages. For a talk based on this paper, see this http URL

http://arxiv.org/abs/1506.03733
A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics
Lee Smolin
(Submitted on 11 Jun 2015)
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
10 pages. Awarded third place in the 2015 FQXi essay contest

===================formatting the above list========================
Indicate the papers you think will prove most significant for future Loop-and-allied QG research. The poll is multiple choice, so it's possible to vote for several. Abstracts follow in the next post.

http://arxiv.org/abs/1504.01065
Wilson loops in CDT quantum gravity
J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll

http://arxiv.org/abs/1504.02169
Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
Alexander Stottmeister, Thomas Thiemann

http://arxiv.org/abs/1504.02170
Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
Alexander Stottmeister, Thomas Thiemann

http://arxiv.org/abs/1504.02171
Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity
Alexander Stottmeister, Thomas Thiemann

http://arxiv.org/abs/1504.02822
Duality between Spin networks and the 2D Ising model
Valentin Bonzom, Francesco Costantino, Etera R. Livine

http://arxiv.org/abs/1504.05352
Black hole spectroscopy from Loop Quantum Gravity models
Aurelien Barrau, Xiangyu Cao, Karim Noui, Alejandro Perez

http://arxiv.org/abs/1504.07559
Loop quantum cosmology: From pre-inflationary dynamics to observations
Abhay Ashtekar, Aurelien Barrau

http://arxiv.org/abs/1504.07100
Quantum Holonomy Theory
Johannes Aastrup, Jesper M. Grimstrup

http://arxiv.org/abs/1505.00223
Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator
Jinsong Yang, Yongge Ma

http://arxiv.org/abs/1505.00225
Graphical method in loop quantum gravity: II. The Hamiltonian constraint and inverse volume operators
Jinsong Yang, Yongge Ma

http://arxiv.org/abs/1505.03119
Computing the Effective Action with the Functional Renormalization Group
Alessandro Codello, Roberto Percacci, Leslaw Rachwal, Alberto Tonero

http://arxiv.org/abs/1505.04088
Gravitational crystal inside the black hole
H. Nikolic

http://arxiv.org/abs/1505.04753
Entanglement equilibrium and the Einstein equation
Ted Jacobson

http://arxiv.org/abs/1506.00299
New scalar constraint operator for loop quantum gravity
Mehdi Assanioussi, Jerzy Lewandowski, Ilkka Mäkinen

http://arxiv.org/abs/1506.01018
Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole
Shohreh Abdolrahimi, Don N. Page

http://arxiv.org/abs/1506.03053
Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
Hal M. Haggard, Muxin Han, Aldo Riello

http://arxiv.org/abs/1506.04749
Coupled intertwiner dynamics - a toy model for coupling matter to spin foam models
Sebastian Steinhaus

http://arxiv.org/abs/1506.08073
Lie Group Cosmology
A. Garrett Lisi

http://arxiv.org/abs/1506.08571
A new realization of quantum geometry
Benjamin Bahr, Bianca Dittrich, Marc Geiller

http://arxiv.org/abs/1506.08794
No fermion doubling in quantum geometry
Rodolfo Gambini, Jorge Pullin

Last edited: Jun 30, 2015
5. Jun 12, 2015

### marcus

For me, the two most interesting papers so far, on this quarter's list are:

http://arxiv.org/abs/1505.04753
Entanglement equilibrium and the Einstein equation
Ted Jacobson
(Submitted on 18 May 2015)
We show that the semiclassical Einstein equation holds if and only if the entanglement entropy in small causal diamonds is stationary at constant volume, when varied from a maximally symmetric vacuum state of geometry and quantum fields. The argument hinges on a conjecture about the variation of the conformal boost energy of quantum fields in small diamonds.
7 pages

[this might remind us of Jacobson's 1995 paper which derived GR from thermodynamic assumptions, as "the Einstein equation of state". it remains a problem what molecules of geometry GR might be the EoS of. Chirco Haggard Riello Rovelli showed the geometric variables of Loop gravity could fill the bill, in their "without hidden variables" paper. Those the theory provides already satisfy Jacobson's conditions so GR could arise as their equation of state.
now, it seems, Jacobson is having another go at showing how Einstein GR arises from thermodynamics. the first paper opened up a fertile area of research and this one may also]

http://arxiv.org/abs/1506.03053
Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
Hal M. Haggard, Muxin Han, Aldo Riello
(Submitted on 9 Jun 2015)
We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces. Euclidean notions such as the normal vector to a face are replaced by Levi-Civita holonomies around each of the tetrahedron's faces. This allows the reconstruction of both spherical and hyperbolic tetrahedra within a unified framework. A new type of hyperbolic simplex is introduced in order for all the sectors encoded in the algebraic data to be covered. Generalizing the phase space of shapes associated to flat tetrahedra leads to group valued moment maps and quasi-Poisson spaces. These discrete geometries provide a natural arena for considering the quantization of gravity including a cosmological constant. A concrete realization of this is provided by the relation with the spin-network states of loop quantum gravity. This work therefore provides a bottom-up justification for the emergence of deformed gauge symmetries and quantum groups in 3+1 dimensional covariant loop quantum gravity in the presence of a cosmological constant.
38 pages and 9 figures

[Einstein's cosmological curvature constant Λ is a homogeneous intrinsic or residual spacetime curvature unrelated to the additional curvatures arising from concentrations of matter and radiation. If Λ is to be included in quantum gravity, it seems reasonable that quantum elements such as simplexes, in particular the tetrahedra, must be cut from homogeneously curved space, not the flat space from which ordinary simplexes are.
Minkowski's classic 1897 theorem relates an algebraic condition---some vectors adding up to zero---to a geometric one: the existence of a polyhedron with those vectors as the area-sized outward normals of its faces. This theorem holds in Euclidean space. Until now it wasn't clear how to extend the theorem to homogeneously curved spaces. New concepts and definitions were needed These authors, HHR, found a way to extend Minkowski's theorem, a longtime essential tool with many uses, to spaces with cosmological constant Λ. In doing so they provide a "bottom-up" understanding of how LQG has extended over the past 4 or 5 years to include Lambda.
BTW another way to talk about "some vectors adding up to zero" is to say they can be arranged head to tail to form a closed polygonal path. That way of stating the condition of the theorem seems easier to generalize from the Euclidean context to uniformly curved spaces.]

Last edited: Jun 13, 2015
6. Jun 13, 2015

### marcus

There are several fascinating things about this paper. One is referred to in the last paragraph on page 1:
"One hundred years later, in 1996, Michael Kapovich and John J. Millson showed how the space of polygons with fixed edge lengths admits a natural phase space structure [35]"
So the Kapovich-Millson paper (a math paper in the area of differential geometry) is an essential part of this.
Polygons (closed chains of segments) can be given a dynamic structure--can have "position and momentum" in the world of polygons.
And Minkowski says polygons determine polyhedra , so polyhedra can acquire a phase space by this reciprocal relationship. (The polygon segments acting as area-sized normals to the polyhedron faces.)
We should have a link to the Kapovich-Millson paper so we can take a look.
https://www.math.ucdavis.edu/~kapovich/EPR/space.pdf
The symplectic geometry of polygons in Euclidean space.
43 pages, 2 figures
This pdf is encoded so that excerpts cannot be quoted or printed out. But it can be read on site.
There is a printable related 1999 paper which recaps it and extends the 1996 result
http://arxiv.org/abs/math/9907143
The symplectic geometry of polygons in hyperbolic 3-space
Michael Kapovich, John J. Millson, Thomas Treloar
and a third, a related 2000 paper, written in a plainer style that might be easier to understand
http://arxiv.org/abs/math/0009193
The Symplectic Geometry of Polygons in the 3-sphere
Thomas Treloar
23 pages.
Notice that as you bend a polygon (with fixed edge lengths) every which way you are in effect pointing the normals of the Minkowski-associated polyhedron in different directions (keeping the areas of the faces fixed) so you could be changing the dihedral angles between faces and even the shapes of the faces. The Minkowski correspondence suggests a wider significance to the Kapovich, Millson, Treloar phase spaces, but can this correspondence be generalized to apply e.g. to the 3-sphere, or to hyperbolic 3-space? If it can, we have a phase space on the world of uniform curved polyhedra, not just polygons-which are merely closed chains of geodesic (i.e. "straight") edges.
Kapovich, Millson, Treloar did not consider the Minkowski correspondence and how to extend their analysis to polyhedra with fixed face areas. This is where Haggard Han Riello come in.

Last edited: Jun 13, 2015
7. Jun 13, 2015

### JorisL

I'm not sure this is open access since I've got access to quite a lot of subscriptions in my dorm.

The Symplectic Geometry of Polygons in Euclidean Space
Michael Kapovich and John J. Millson

We study the symplectic geometry of moduli spaces Mr of polygons with fixed side lengths in Euclidean space. We show that Mr has a natural structure of a complex analytic space and is complex-analytically isomorphic to the weighted quotient of ( 5 2 ) n by PLS(2,C) constructed by Deligne and Mostow. We study the Hamiltonian flows on Mr obtained by bending the polygon along diagonals and show the group generated by such flows acts transitively on Mr. We also relate these flows to the twist flows of Goldman
and Jeffrey-Weitsman.

Upon further googling I found a link to the article on the website of Michael Kapovich.

If I understand correctly they are able to associate a manifold with the polygon space. Then they show it is symplectic and if my understanding is complete that is sufficient to have a phase space structure (I only had a brief introduction to differential geometry in the context of classical mechanics semi-rigorous).
After this is established the powerful differential geometry machinery can be used.

8. Jun 14, 2015

### marcus

Hi Joris, thanks for posting the pointers to work by Kapovich and Millson. I somehow missed seeing your post until I had been finding links on my own to add to the previous post #6. So I inadvertently duplicated one of yours---to Kapovich's UC Davis website.

This paper by Haggard Han Riello (HHR) is part of a major development in quantum gravity which is outlined (with citations to a dozen or so papers) in the introduction to the "compact phase space" paper of Rovelli and Vidotto, which I think was pretty clearly the most interesting one in this thread's first quarter poll.

It gives a useful overview of what's happening so I'll quote at length. This is from the introduction of:
http://arxiv.org/abs/1502.00278
Compact phase space, cosmological constant, discrete time
Carlo Rovelli and Francesca Vidotto
=quote=
The presence of the cosmological constant can affect the quantum kinematics of gravity. Here we show that it enters naturally in loop quantum gravity (LQG) by determining the size of a compact phase space and the dimension of the corresponding finite dimensional Hilbert space. This yields the discretization of the extrinsic curvature and can be related to time discreetness.

Recent results indicate that a positive cosmological constant simplifies, rather than complicating, our understanding of quantum gravity. Fairbairn and Meusburger [1] and Han [2–4], building on [5, 6] and [7], have shown that the cosmological constant makes covariant LQG finite. Haggard, Han, Kamin ́ski and Riello [8] have given a straightforward construction of the LQG dynamics in the presence of the cosmological constant, related to the geometry of constant curvature triangulations, a key idea introduced by Bahr and Dittrich [9], which grounds the present work. The LQG kinematics needs to be modified to take into account the presence of a cosmological constant; this was realised long ago by Borissov, Major and Smolin [10–12] and the problem has been recently explored in detail by Dupius, Girelli, Livine and Bonzom [13–16] for negative cosmological constant.

A discretization of spacetime in terms of flat simplices is not suitable for a theory with cosmological constant because flat geometry solves the field equations only with vanishing cosmological constant. This problem can be solved choosing a discretization with simplices with constant curvature. Here we show with a positive cosmological constant, a constant curvature discretization leads to a modification of the LQG phase space...
==endquote==
At the very end of the Rovelli Vidotto (February 2015) paper they mention work written up in this one by HHR which just came out.
==quote==
Note: We understand that Han, Haggard, Kamin ́sky and Riello have related results in 3+1 dimensions, which will appear soon.
==endquote==
"Soon" turned out to be June, four months later, and there were just three authors, with Kaminsky's active collaboration early on mentioned favorably in the acknowledgments. The HHR paper we are looking at now is clearly what that Note refers to. We've been waiting for it

Last edited: Jun 14, 2015
9. Jun 14, 2015

### marcus

The overview given in the February 2015 Rovelli Vidotto paper gives context for understanding a key sentence in the HHR abstract indicating the significance of their paper:
http://arxiv.org/abs/1506.03053
Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
Hal M. Haggard, Muxin Han, Aldo Riello
(Submitted on 9 Jun 2015)
We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces. Euclidean notions such as the normal vector to a face are replaced by Levi-Civita holonomies around each of the tetrahedron's faces. This allows the reconstruction of both spherical and hyperbolic tetrahedra within a unified framework. A new type of hyperbolic simplex is introduced in order for all the sectors encoded in the algebraic data to be covered. Generalizing the phase space of shapes associated to flat tetrahedra leads to group valued moment maps and quasi-Poisson spaces. These discrete geometries provide a natural arena for considering the quantization of gravity including a cosmological constant. A concrete realization of this is provided by the relation with the spin-network states of loop quantum gravity. This work therefore provides a bottom-up justification for the emergence of deformed gauge symmetries and quantum groups in 3+1 dimensional covariant loop quantum gravity in the presence of a cosmological constant.
38 pages and 9 figures

Rovelli Vidotto give references to earlier work by Fairbairn Muesberger and by Han (I'm probably leaving others out) where they introduce quantum groups in a TOP DOWN way to include the cosmological constant in LQG. In fact this goes way back, have to refer to that R&V overview. In those earlier papers it seemed to work but appeared to come out of the blue. Now with the HHKR and HHR papers it seems understandable that it HAD TO BE that way---they give a bottom-up justification and, in a sense a hint as what the cosmological constant IS---relating it to compact phase space, finite dimensional Hilbert space, discrete time.

10. Jun 26, 2015

### marcus

Candidate papers for the 2nd quarter MIP poll:
http://arxiv.org/abs/1504.01065
Wilson loops in CDT quantum gravity
J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll
(Submitted on 4 Apr 2015)
By explicit construction, we show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We use this set-up to investigate a class of Wilson line observables associated with the world line of a point particle coupled to quantum gravity, and deduce from their expectation values that the underlying holonomies cover the group manifold of SO(4) uniformly.
30 pages, 5 figures

http://arxiv.org/abs/1504.02169
Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework, and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g. spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article, and its companion, affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

http://arxiv.org/abs/1504.02170
Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G=U(1)n and support by numerical evidence for G=SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation, that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask, whether a similar connection exists for compact Lie groups, as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.

http://arxiv.org/abs/1504.02171
Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity
Alexander Stottmeister, Thomas Thiemann
(Submitted on 9 Apr 2015)
In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.

http://arxiv.org/abs/1504.02822
Duality between Spin networks and the 2D Ising model
Valentin Bonzom, Francesco Costantino, Etera R. Livine
(Submitted on 11 Apr 2015)
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories which couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
35 pages

http://arxiv.org/abs/1504.05352
Black hole spectroscopy from Loop Quantum Gravity models
Aurelien Barrau, Xiangyu Cao, Karim Noui, Alejandro Perez
(Submitted on 21 Apr 2015)
Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter γ. Starting with black holes of initial horizon area A∼102 in Planck units, we present the spectra for different values of γ. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that γ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.
11 pages, 9 figures

http://arxiv.org/abs/1504.07559
Loop quantum cosmology: From pre-inflationary dynamics to observations
Abhay Ashtekar, Aurelien Barrau
(Submitted on 28 Apr 2015)
The Planck collaboration has provided us rich information about the early universe, and a host of new observational missions will soon shed further light on the anomalies' that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.
20 pages, 5 figures. Invited review article for the "focus issue" of Classical and Quantum Gravity : "Planck and the fundamentals of cosmology"

http://arxiv.org/abs/1504.07100
Quantum Holonomy Theory
Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 27 Apr 2015)
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit.
76 pages, 6 figures

http://arxiv.org/abs/1505.00223
Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator
Jinsong Yang, Yongge Ma
(Submitted on 1 May 2015)
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In the series of papers, we will introduce a graphical method, developed by Yutsis and Brink, to loop quantum gravity. The graphical method provides a very powerful technique for simplifying complicated calculations. In this first paper, the closed formula of volume operator is derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the acting of operators as well as the spin network states, we use the simple rules for transforming graphs to yield the resulting formula. Comparing with the complicated algebraic derivation in some literatures, our procedure is more concise, intuitive and visual. The resulting matrix elements of volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin network states.
40 pages

http://arxiv.org/abs/1505.00225
Graphical method in loop quantum gravity: II. The Hamiltonian constraint and inverse volume operators
Jinsong Yang, Yongge Ma
(Submitted on 1 May 2015)
This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Hamiltonian constraint operator and the so-called inverse volume operator on spin network states with trivalent vertices. Both of the operators involve the co-triad operator which contains holonomies by construction. The non-ambiguous, concise and visual characters of our graphical method ensure the rigour for our calculations. Our results indicate some corrections to the existing results in literatures for both operators.
19 pages

http://arxiv.org/abs/1505.03119
Computing the Effective Action with the Functional Renormalization Group
Alessandro Codello, Roberto Percacci, Leslaw Rachwal, Alberto Tonero
(Submitted on 12 May 2015)
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action Γk. The ordinary effective action Γ0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We use the results of Barvinsky, Vilkovisky and Avramidi on the non-local heat kernel coefficients to reproduce the four point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
40 pages

http://arxiv.org/abs/1505.04088
Gravitational crystal inside the black hole
H. Nikolic
(Submitted on 15 May 2015)
Crystals, as quantum objects typically much larger than their lattice spacing, are a counterexample to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black-hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.
6 pages

http://arxiv.org/abs/1505.04753
Entanglement equilibrium and the Einstein equation
Ted Jacobson
(Submitted on 18 May 2015)
We show that the semiclassical Einstein equation holds if and only if the entanglement entropy in small causal diamonds is stationary at constant volume, when varied from a maximally symmetric vacuum state of geometry and quantum fields. The argument hinges on a conjecture about the variation of the conformal boost energy of quantum fields in small diamonds.
7 pages

http://arxiv.org/abs/1506.00299
New scalar constraint operator for loop quantum gravity
Mehdi Assanioussi, Jerzy Lewandowski, Ilkka Mäkinen
(Submitted on 31 May 2015)
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of these operators on a general level.
14 pages.

http://arxiv.org/abs/1506.01018
Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole
Shohreh Abdolrahimi, Don N. Page
(Submitted on 2 Jun 2015)
Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.
17 pages.

http://arxiv.org/abs/1506.03053
Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
Hal M. Haggard, Muxin Han, Aldo Riello
(Submitted on 9 Jun 2015)
We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces. Euclidean notions such as the normal vector to a face are replaced by Levi-Civita holonomies around each of the tetrahedron's faces. This allows the reconstruction of both spherical and hyperbolic tetrahedra within a unified framework. A new type of hyperbolic simplex is introduced in order for all the sectors encoded in the algebraic data to be covered. Generalizing the phase space of shapes associated to flat tetrahedra leads to group valued moment maps and quasi-Poisson spaces. These discrete geometries provide a natural arena for considering the quantization of gravity including a cosmological constant. A concrete realization of this is provided by the relation with the spin-network states of loop quantum gravity. This work therefore provides a bottom-up justification for the emergence of deformed gauge symmetries and quantum groups in 3+1 dimensional covariant loop quantum gravity in the presence of a cosmological constant.
38 pages and 9 figures

http://arxiv.org/abs/1506.08073
Lie Group Cosmology
A. Garrett Lisi
(Submitted on 24 Jun 2015)
Our universe is a deforming Lie group.
42 pages, 1 figure

http://arxiv.org/abs/1506.04749
Coupled intertwiner dynamics - a toy model for coupling matter to spin foam models
Sebastian Steinhaus
The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretisation. However extracting this mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories.
Therefore, we introduce a simple 2D toy model for Yang--Mills coupled to spin foams, namely an Ising model coupled to so--called intertwiner models defined for SU(2)k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretisation. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.
31 + 6 pages, 8 figures, 7 tables

http://arxiv.org/abs/1506.08571
A new realization of quantum geometry
Benjamin Bahr, Bianca Dittrich, Marc Geiller
(Submitted on 29 Jun 2015)
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states are built upon it by creating local curvature excitations. The inner product induces a discrete topology on the gauge group, which turns out to be an essential ingredient for the construction of a continuum limit Hilbert space. This leads to a representation of the full holonomy-flux algebra of loop quantum gravity which is unitarily-inequivalent to the one based on the Ashtekar-Isham-Lewandowski vacuum. It therefore provides a new notion of quantum geometry. We discuss how the spectra of geometric operators, including holonomy and area operators, are affected by this new quantization. In particular, we find that the area operator is bounded, and that there are two different ways in which the Barbero-Immirzi parameter can be taken into account. The methods introduced in this work open up new possibilities for investigating further realizations of quantum geometry based on different vacua.
72 pages, 6 figures

http://arxiv.org/abs/1506.08794
No fermion doubling in quantum geometry
Rodolfo Gambini, Jorge Pullin
(Submitted on 29 Jun 2015)
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main effect of the quantum geometry is to discretize the equations of matter fields. This raises the possibility that in the case of fermion fields one could confront the usual fermion doubling problem that arises in lattice gauge theories. We suggest, again based on recent results on spherical symmetry, that since the background space-times will generically involve superpositions of states associated with different discretizations the phenomenon may not arise. This opens a possibility of incorporating chiral fermions in the framework of loop quantum gravity.
2 pages.

Last edited: Jun 30, 2015