Large N Matrix Hyperspheres and the Gauge-Gravity Correspondence

TL;DR

This paper explores the large N dynamics of multi-matrix systems in zero dimensions, revealing a new repulsive potential and eigenvalue distributions that relate to the gauge-gravity correspondence in AdS/CFT.

Contribution

It derives the large N behavior of multi-matrix models, showing a novel logarithmic repulsion and eigenvalue support structure, extending understanding beyond single matrix cases.

Findings

Eigenvalue density forms a hyper annulus due to repulsive potential

Single matrix case yields Wigner-type eigenvalue distribution

Connection established between matrix eigenvalues and AdS/CFT parameters

Abstract

The large N dynamics of a subsector of d=0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, as a result of which the density of radial eigenvalues has support on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom of the Yang-Mills interaction can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.