Exact Renormalisation Group Equations and Loop Equations for Tensor Models

TL;DR

This paper reviews and applies exact renormalisation group and loop equations to tensor models and tensorial group field theories, deriving expectation values and establishing scaling dimensions.

Contribution

It introduces formulations of renormalisation group and loop equations for tensor models, providing new tools for analyzing their behavior and interactions.

Findings

Derived leading order expectation values of observables.

Established a scaling dimension for interactions in Abelian tensorial group field theories.

Presented analogues of loop equations for tensor models.

Abstract

In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading order expectation values of observables in tensor models. Furthermore, we use the exact renormalisation group equations to establish a suitable scaling dimension for interactions in Abelian tensorial group field theories with a closure constraint. We also present analogues of the loop equations for tensor models.