Submatrix deconfinement and small black holes in AdS

TL;DR

This paper investigates the microcanonical ensemble of large N matrix models at intermediate energies, revealing a partial deconfinement phase with submatrix degrees of freedom, and discusses implications for small black holes in AdS space.

Contribution

It provides evidence for a partial deconfinement phase involving submatrix degrees of freedom and illustrates a smooth transition from strings to black holes in AdS.

Findings

Identification of a partial deconfinement phase with submatrix excitation energies of order M^2

Evidence for phase separation of degrees of freedom in the coexistence region

Discussion of implications for small black holes in AdS space

Abstract

Large $N$ gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order $N^2$ at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies $1<<E<<N^2$ in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a $U(M)$ subgroup of $U(N)$, with $M<<N$ have an excitation energy of order $M^2$ and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in $AdS$ are discussed.