City Research Online

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 N = 4SYM.

Publication Type:	Article
Additional Information:	Open Access . This article is distributed under the terms of the Copyright © 2026, The Author(s). Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords:	Matrix Models, AdS-CFT Correspondence, Black Holes in String Theory
Subjects:	Q Science Q Science > QA Mathematics Q Science > QB Astronomy Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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