An analysis of the intermediate field theory of $T^4$ tensor model

TL;DR

This paper investigates the intermediate field theory of a $T^4$ tensor model, deriving key equations to understand the eigenvalue distributions of associated matrices.

Contribution

It provides a detailed analysis of the saddle point and Schwinger-Dyson equations for the tensor model's intermediate field representation, revealing eigenvalue behavior.

Findings

Derived saddle point equation and Schwinger-Dyson constraints

Described leading and next-to-leading eigenvalue distributions

Analyzed the multi-matrix model structure

Abstract

In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then use them to describe the leading and next-to-leading eigenvalues distribution of the matrices.