Near commuting multi-matrix models

TL;DR

This paper studies the eigenvalue distribution in Yang-Mills matrix models, showing that under strong coupling, matrices commute and eigenvalues are uniformly distributed within a sphere, with results supported by numerical simulations.

Contribution

It provides an analytical description of eigenvalue distributions in multi-matrix models with complex couplings, extending understanding of their radial extent and commutativity properties.

Findings

Eigenvalues confined to a sphere of radius (3Pi/2g)^(1/3) at strong coupling

Commuting matrices describe the leading order behavior in the Gaussian model

Perturbative analysis aligns with numerical simulation results

Abstract

We investigate the radial extent of the eigenvalue distribution for Yang-Mills type matrix models. We show that, a three matrix Gaussian model with complex Myers coupling, to leading order in strong coupling is described by commuting matrices whose joint eigenvalue distribution is uniform and confined to a ball of radius R=(3Pi/2g)^(1/3). We then study, perturbatively, a 3-component model with a pure commutator action and find a radial extent broadly consistent with numerical simulations.