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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
Universality for Random Tensors
, 2013
"... We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N D independent, identically distributed, complex random variables converges in distribution in the large N limit to the same limit as the distributional limit of a Gaussia ..."
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We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N D independent, identically distributed, complex random variables converges in distribution in the large N limit to the same limit as the distributional limit of a Gaussian tensor model. This generalizes the universality of random matrices to random tensors. We then prove a second, stronger, universality result. Under the weaker assumption that the joint probability distribution of tensor entries is invariant, assuming that the cumulants of this invariant distribution are uniformly bounded, we prove that in the large N limit the tensor again converges in distribution to the distributional limit of a Gaussian tensor model. We emphasize that the covariance of the large N Gaussian is not universal, but depends strongly on the details of the joint distribution. 1
Borel summability and the non perturbative 1/N expansion of arbitrary quartic tensor models
, 2014
"... We extend the proof of Borel summability of melonic quartic tensor models to tensor models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and new bounds based on CauchySchwarz inequalities. The Bo ..."
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Cited by 5 (1 self)
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We extend the proof of Borel summability of melonic quartic tensor models to tensor models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and new bounds based on CauchySchwarz inequalities. The Borel summability is proven to be uniform as the tensor size becomes large. Furthermore, we show that the 1/N expansion of any quartic tensor model can be performed at the constructive level, that is we show that every cumulant is a sum of explicit terms up to some order plus a rest term which is an analytic function in the coupling constant in a cardioid domain of the complex plane and which is suppressed in 1/N.
Renormalization of latticeregularized quantum gravity models I. General considerations
, 2014
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Closed equations of the twopoint functions for tensorial group field theory
"... group field theory ..."
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A combinatorial noncommutative Hopf algebra of graphs
, 2013
"... A noncommutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a noncommutative Hopf algebra for graphs. In order to define a noncommutative product we use a quant ..."
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A noncommutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a noncommutative Hopf algebra for graphs. In order to define a noncommutative product we use a quantum field theoretical (QFT) idea, namely the one of introducing discrete scales on each edge of the graph (which, within the QFT framework, corresponds to energy scales of the associated propagators). Finally, we analyze the associated quadricoalgebra and codendrifrom structures.
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