Eigenvalue Dynamics for Multimatrix Models

TL;DR

This paper investigates eigenvalue dynamics within a specific sector of two matrix models related to ${ m f N}=4$ super Yang-Mills theory, revealing a generalized Van der Monde determinant and connecting to supergravity solutions.

Contribution

It demonstrates that a sector of the two matrix model can be reduced to eigenvalue dynamics and introduces a generalized Van der Monde determinant relevant to this reduction.

Findings

Evidence of eigenvalue reduction in the $SU(2)$ sector

Introduction of a generalized Van der Monde determinant

Connection between matrix observables and supergravity solutions

Abstract

By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the $SU(2)$ sector of ${\cal N}=4$ super Yang-Mills theory, that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the BPS operators of the $SU(2)$ sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.