Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra

TL;DR

This paper develops a new orthogonal basis for gauge invariant operators in free matrix field theories using Brauer algebra, extending previous work to multiple matrices and exploring implications for N=4 SYM quantum mechanics.

Contribution

It introduces a novel basis for multi-matrix gauge invariant operators based on Brauer algebra, generalizing prior single-matrix results and analyzing conserved quantities in related quantum mechanics.

Findings

Orthogonal basis constructed using Brauer algebra for multi-matrix operators

Identification of conserved operators in N=4 SYM quantum mechanics

Extension of previous single-matrix results to multi-matrix case

Abstract

We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a signle complex matrix. We also discuss the matrix quantum mechanics relevant to N=4 SYM on S^{3} times R. A commuting set of conserved operators whose eigenstates are given by the orthogonal basis is shown by using enhanced symmetries at zero coupling.