Universality of Heavy Operators in Matrix Models

TL;DR

This paper demonstrates that in a simple two matrix model at strong coupling, heavy operators exhibit universal eigenvalue distributions and correlation functions, revealing a black hole-like regime with phase boundaries and Abelianization phenomena.

Contribution

It establishes the existence of a universal black hole regime in a two matrix model at strong coupling, extending previous findings and identifying phase boundaries and Abelianization effects.

Findings

Universal eigenvalue densities are parabola-shaped in the black hole regime.

Correlation functions are determined by a few parameters in the universal regime.

A phase boundary separates universal and non-universal regimes, with Abelianization occurring in the latter.

Abstract

In large $N$ theories with a gravity dual, generic heavy operators should be dual to black holes in the bulk. The microscopic details of such operators should then be irrelevant in the low energy theory. We look for such universality in the strong coupling limit of a very simple two matrix model -- the Hoppe model. Using analytics as well as Monte Carlo simulations, we show that there exists a universal black hole regime where the eigenvalue densities are given by parabolas and the correlation functions of probes in these backgrounds are completely determined by a few parameters. An important feature of strong coupling in this model is that the matrices commute and one can define joint eigenvalue distributions which also exhibit universality. These two results extend the beautiful findings of Berenstein, Hanada and Hartnoll. Not all heavy operators are universal and at strong coupling there is a sharp phase boundary between the universal and non universal regimes (Of course this should not be confused with the universality of eigenvalue spacing in matrix models). Moreover, in the non universal phase, we also find an interesting phenomenon we call Abelianization where some eigenvalues run off to infinity, reminiscent of heavy dual giant gravitons in $\mathcal N=4$ SYM.