Borel summability and the non perturbative $1/N$ expansion of arbitrary quartic tensor models
Year: 2014
Type: preprint
Abstract: 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 Cauchy-Schwarz 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 $1/N$.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W54326031