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21
Quantum Gravity and Renormalization: The Tensor Track
 AIP Conf. Proc. 1444, 18 (2011) [arXiv:1112.5104 [hepth
"... We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches. LPT20XXxx ..."
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We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches. LPT20XXxx
Discrete Gravity Models and Loop Quantum Gravity: a Short Review
 SIGMA
, 2012
"... We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the ..."
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Cited by 6 (0 self)
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We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.
Group field theories for all loop quantum gravity
"... Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories ..."
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Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the gft formulation of the kkl spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes. 1
The Tensor Track, III
, 2013
"... We provide an informal uptodate review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (GromovHausdorff limit, Loop vertex expansion, ..."
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We provide an informal uptodate review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (GromovHausdorff limit, Loop vertex expansion, OsterwalderSchrader positivity...) which, while important for the tensor track program, are not detailed in the usual quantum gravity literature. We list open questions in the conclusion and provide a rather extended bibliography.
The Construction of Spin Foam Vertex Amplitudes
, 2013
"... Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4dimensional generalization of the Ponzano–Regge model for ..."
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Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4dimensional generalization of the Ponzano–Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentzinvariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.
Melons are branched polymers
, 2013
"... Melonic graphs constitute the family of graphs arising at leading order in the 1/N expansion of tensor models. They were shown to lead to a continuum phase, reminiscent of branched polymers. We show here that they are in fact precisely branched polymers, that is, they possess Hausdorff dimension 2 a ..."
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Melonic graphs constitute the family of graphs arising at leading order in the 1/N expansion of tensor models. They were shown to lead to a continuum phase, reminiscent of branched polymers. We show here that they are in fact precisely branched polymers, that is, they possess Hausdorff dimension 2 and spectral dimension 4/3. 1
Asymptotic Analysis of the Ponzano–Regge Model with NonCommutative Metric Boundary Data?
"... Abstract. We apply the noncommutative Fourier transform for Lie groups to formulate the noncommutative metric representation of the Ponzano–Regge spin foam model for 3d quantum gravity. The noncommutative representation allows to express the amplitudes of the model as a first order phase space pa ..."
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Abstract. We apply the noncommutative Fourier transform for Lie groups to formulate the noncommutative metric representation of the Ponzano–Regge spin foam model for 3d quantum gravity. The noncommutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semiclassical limit. First, we compare the stationary phase equations in the classical limit for three different noncommutative structures corresponding to the symmetric, Duflo and Freidel–Livine–Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for noncommutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the noncommutative metric representation facilitates a convenient semiclassical analysis of the Ponzano–Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6jsymbol using the noncommutative phase space path integral for the Ponzano–Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states. Key words: Ponzano–Regge model; noncommutative representation; asymptotic analysis
On the relations between gravity and BF theories
"... Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action. ..."
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Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action.