Multiscale Loop Vertex Expansion for Cumulants, the $T_3^4$ Model

TL;DR

This paper develops a multiscale loop vertex expansion method to analyze cumulants of a tensor field theory with a quartic interaction, establishing their analyticity and Borel summability.

Contribution

It introduces a novel multiscale loop vertex expansion approach for tensor field theories, proving key properties of cumulants.

Findings

Proved analyticity of cumulants up to finite order.

Established Borel summability of cumulants.

Constructed cumulants for the $T_3^4$ tensor model.

Abstract

We construct cumulants up to a finite order of a tensor field theory perturbed by a quartic term, nicknamed the $T_3^4$ model. The method we use is the multi-scale loop vertex expansion. We prove analyticity and Borel summability of the cumulants up to finite order.