Finite temperature effective action, AdS_5 black holes, and 1/N expansion

TL;DR

This paper introduces a matrix model for string theory in AdS_5 imes S_5 that captures black hole nucleation, phase transitions, and the Hagedorn divergence, providing insights into the thermodynamics of the system.

Contribution

It presents a phenomenological matrix model that reproduces qualitative features of AdS_5 imes S_5 string theory, including phase transitions and black hole dynamics.

Findings

Identification of a critical temperature for a phase transition.

Description of the Hagedorn divergence as a saddle point merger.

Prediction of a Gross-Witten phase transition at the critical temperature.

Abstract

We propose a phenomenological matrix model to study string theory in AdS_5 \times S_5 in the canonical ensemble. The model reproduces all the known qualitative features of the theory. In particular, it gives a simple effective potential description of Euclidean black hole nucleation and the tunnelling between thermal AdS and the big black hole. It also has some interesting predictions. We find that there exists a critical temperature at which the Euclidean small black hole undergoes a Gross-Witten phase transition. We identify the phase transition with the Horowitz-Polchinski point where the black hole horizon size becomes comparable to the string scale. The appearance of the Hagedorn divergence of thermal AdS is due to the merger of saddle points corresponding to the Euclidean small black hole and thermal AdS. The merger can be described in terms of a cusp (A_3) catastrophe and divergences at the perturbative string level are smoothed out at finite string coupling using standard techniques of catastrophe theory.