Correlation functions of just renormalizable tensorial group field theory: The melonic approximation

TL;DR

This paper investigates the Schwinger-Dyson equations in tensorial group field theory, focusing on the melonic approximation to understand correlation functions in the large N limit.

Contribution

It derives master equations for correlation functions in the tensorial -model and analyzes their solutions within the melonic approximation, advancing understanding of tensor models.

Findings

Derived master equations for two- and four-point functions

Analyzed solutions in the melonic approximation

Enhanced understanding of large N tensor model behavior

Abstract

The $D$-colored version of tensor models has been shown to admit a large $N$-limit expansion. The leading contributions result from so-called melonic graphs which are dual to the $D$-sphere. This is a note about the Schwinger-Dyson equations of the tensorial $\varphi^{4}_{5}$-model (with propagator $1/{\bf p}^{2}$) and their melonic approximation. We derive the master equations for two- and four-point correlation functions and discuss their solution.