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arXiv · 1403.0170

Universality and Borel Summability of Arbitrary Quartic Tensor Models

Thibault Delepouve·Razvan Gurau·Vincent Rivasseau
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Abstract

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 $1/N$. Together with the existence of the large $N$ limit of the second cumulant, this proves that the corresponding sequence of probability measures is uniformly bounded and obeys the tensorial universality theorem.

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Thibault Delepouve, Razvan Gurau, Vincent Rivasseau. 2014-03-02. Universality and Borel Summability of Arbitrary Quartic Tensor Models. https://arxiv.org/abs/1403.0170

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