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2014

Universality and Borel Summability of Arbitrary Quartic Tensor Models

Delepouve, Thibault, Gurau, Razvan, Rivasseau, Vincent

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We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions.

This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated Cauchy-Schwarz inequalities.
Borel summability is proven, uniformly as the tensor size $N$ becomes large.
Every cumulant is written as a sum of explicitly calculated terms plus a remainder, suppressed in $1/N$.

Universality and Borel Summability of Arbitrary Quartic Tensor Models · Around

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2011

Cited alongside, same era.

R. Gurau, “The 1/N expansion of colored tensor models,” Annales Henri Poincare 12

2011

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R. Gurau and V. Rivasseau, “The 1/N expansion of colored tensor models in arbitrary dimension,” Europhys. Lett. 95

2011

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V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, “Critical behavior of colored tensor models in the large N limit,” Nucl. Phys. B 853

2011

Cited alongside, same era.

R. Gurau, G. Schaeffer “Regular colored graphs of positive degree,” [arXiv:1307.5279 [math.CO]]

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V. Bonzom and F. Combes, “Fully packed loops on random surfaces and the 1/N expansion of tensor models,” arXiv:1304.4152 [hep-th]

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A. Baratin, S. Carrozza, D. Oriti, J. P. Ryan and M. Smerlak, “Melonic phase transition in group field theory,” arXiv:1307.5026 [hep-th]

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V. Rivasseau, “The Tensor Track, III,” arXiv:1311.1461 [hep-th]

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2013

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V. Bonzom, “Revisiting random tensor models at large N via the Schwinger-Dyson equations,” JHEP 1303

2013

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V. Bonzom, “New 1/N expansions in random tensor models,” JHEP 1306

2013

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