Correlation functions and representation bases in free N=4 Super Yang-Mills

TL;DR

This paper investigates exact correlation functions in free N=4 Super Yang-Mills theory, introducing a Brauer algebra-based basis for multi-matrix operators and analyzing their three-point functions with exact N-dependence.

Contribution

It develops a new basis for multi-matrix operators using Brauer algebras, extending previous work, and computes exact multi-point functions including three-point functions of BPS operators.

Findings

Three-point functions are governed by Brauer algebra branching rules.

Correlation functions exhibit a factorized form under certain representation relations.

Exact N-dependence of multi-point functions is explicitly computed.

Abstract

We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the construction of representation bases from the viewpoint of the enhanced symmetry structure of the free theory. We present a basis of multi-matrix models using elements of Brauer algebras, generalising our previous construction for two matrices. We will compute multi-point functions of the basis with the exact N-dependence. In particular we study three-point functions of a class of BPS operators, and we find that they are given by a branching rule of the Brauer algebra. The three-point functions take a factorised form if representations on the operators satisfy a relation.