# Our picks for second quarter 2011 MIP (most important QG paper)

## Which paper(s) will prove most valuable to future research?

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1. Jul 5, 2011

### marcus

Of these twelve candidates, please choose the paper or papers which you think will contribute most significantly to future quantum gravity research. Since multiple choices are possible in the poll, you may select several papers. Abstract summaries follow in the next post.

Holonomy observables in Ponzano-Regge type state sum models
John W. Barrett, Frank Hellmann
http://arxiv.org/abs/1106.6016
http://arxiv.org/cits/1106.6016

Towards Loop Quantization of Plane Gravitational Waves
Franz Hinterleitner, Seth Major
http://arxiv.org/abs/1106.1448
http://arxiv.org/cits/1106.1448

Towards Loop Quantum Supergravity (LQSG)
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
http://arxiv.org/abs/1106.1103
http://arxiv.org/cits/1106.1103

Relative locality: A deepening of the relativity principle
Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin
http://arxiv.org/abs/1106.0313
http://arxiv.org/cits/1106.0313

Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations
Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner
http://arxiv.org/abs/1105.5646
http://arxiv.org/cits/1105.5646

Spectral Action for Robertson-Walker metrics
Ali H. Chamseddine, Alain Connes
http://arxiv.org/abs/1105.4637
http://arxiv.org/cits/1105.4637

New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
http://arxiv.org/abs/1105.3703
http://arxiv.org/cits/1105.3703

Spinor Representation for Loop Quantum Gravity
Etera R. Livine, Johannes Tambornino
http://arxiv.org/abs/1105.3385
http://arxiv.org/cits/1105.3385

Critical behavior of colored tensor models in the large N limit
Valentin Bonzom, Razvan Gurau, Aldo Riello, Vincent Rivasseau
http://arxiv.org/abs/1105.3122
http://arxiv.org/cits/1105.3122

Cosmological Constant in LQG Vertex Amplitude
Muxin Han
http://arxiv.org/abs/1105.2212
http://arxiv.org/cits/1105.2212

A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
Eugenio Bianchi, Carlo Rovelli
http://arxiv.org/abs/1105.1898
http://arxiv.org/cits/1105.1898

Effective Hamiltonian Constraint from Group Field Theory
Etera R. Livine, Daniele Oriti, James P. Ryan
http://arxiv.org/abs/1104.5509
http://arxiv.org/cits/1104.5509

2. Jul 5, 2011

### marcus

Holonomy observables in Ponzano-Regge type state sum models
John W. Barrett, Frank Hellmann
http://arxiv.org/abs/1106.6016
http://arxiv.org/cits/1106.6016
We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels. We elucidate this interpretation by showing how they arise from the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.
5 pages, 2 figures

Towards Loop Quantization of Plane Gravitational Waves
Franz Hinterleitner, Seth Major
http://arxiv.org/abs/1106.1448
http://arxiv.org/cits/1106.1448
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

Towards Loop Quantum Supergravity (LQSG)
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
http://arxiv.org/abs/1106.1103
http://arxiv.org/cits/1106.1103
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

Relative locality: A deepening of the relativity principle
Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin
http://arxiv.org/abs/1106.0313
http://arxiv.org/cits/1106.0313
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 GN may be neglected, while their ratio, the Planck mass Mp = sqrt[hbar/GN], is important. We propose that Mp 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

Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations
Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner
http://arxiv.org/abs/1105.5646
http://arxiv.org/cits/1105.5646
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.
5 pages, 3 figures

Spectral Action for Robertson-Walker metrics
Ali H. Chamseddine, Alain Connes
http://arxiv.org/abs/1105.4637
http://arxiv.org/cits/1105.4637
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.
28 pages

New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
http://arxiv.org/abs/1105.3703
http://arxiv.org/cits/1105.3703
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

Spinor Representation for Loop Quantum Gravity
Etera R. Livine, Johannes Tambornino
http://arxiv.org/abs/1105.3385
http://arxiv.org/cits/1105.3385
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to represent these spinors is the Bargmann space of holomorphic square-integrable functions over complex numbers. We show the unitary equivalence between the resulting generalized Bargmann space and the standard loop quantum gravity Hilbert space by explicitly constructing the unitary map. The latter maps SU(2)-holonomies, when written as a function of spinors, to their holomorphic part. We analyze the properties of this map in detail. We show that the subspace of gauge invariant states can be characterized particularly easy in this representation of loop gravity. Furthermore, this map provides a tool to efficiently calculate physical quantities since integrals over the group are exchanged for straightforward integrals over the complex plane.
37 pages

Critical behavior of colored tensor models in the large N limit
Valentin Bonzom, Razvan Gurau, Aldo Riello, Vincent Rivasseau
http://arxiv.org/abs/1105.3122
http://arxiv.org/cits/1105.3122
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.
20 pages

Cosmological Constant in LQG Vertex Amplitude
Muxin Han
http://arxiv.org/abs/1105.2212
http://arxiv.org/cits/1105.2212
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity). We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with cosmological constant (in the corresponding 4-simplex). In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.
6 pages, 5 figures

A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
Eugenio Bianchi, Carlo Rovelli
http://arxiv.org/abs/1105.1898
http://arxiv.org/cits/1105.1898
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance $1/\sqrt{\Lambda}$ related the cosmological constant Lambda.
This yields a simple geometrical interpretation for the relation between the quantum deformation parameter
$$q=e^{i \Lambda l_{Planck}^2}$$
and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.
2 pages, 1 figure

Effective Hamiltonian Constraint from Group Field Theory
Etera R. Livine, Daniele Oriti, James P. Ryan
http://arxiv.org/abs/1104.5509
http://arxiv.org/cits/1104.5509
Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the group field theory action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions. We apply our procedure to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of group field theories.
14 pages

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Last edited: Jul 5, 2011