On the large N limit of the Schwinger-Dyson equation of tensor field theory

TL;DR

This paper investigates the large N behavior of Schwinger-Dyson equations in a rank-3 tensor quantum field theory, establishing scalings for a well-defined limit and verifying results perturbatively.

Contribution

It identifies the correct N-scaling for tensor field theory Schwinger-Dyson equations and confirms the analysis through second-order perturbative checks.

Findings

Established N-scaling for tensor Schwinger-Dyson equations

Validated the scaling with second-order perturbative calculations

Provided a framework for analyzing large N limits in tensor theories

Abstract

We analyse in this paper the large N limit of the Schwinger-Dyson equations in a rank-3 tensor quantum field theory, which are derived with the help of Ward-Takahashi identities. In order to have a well-defined large N limit, appropriate scalings in powers of N for the various terms present in the action are explicitly found. A perturbative check of our results is done, up to second order in the coupling constant.