Large $N$ phase transitions and the fate of small Schwarzschild-AdS black holes

TL;DR

This paper investigates the instability and evolution of small Schwarzschild-AdS black holes in a specific spacetime, exploring their holographic duals in large-N supersymmetric Yang-Mills theory and addressing related theoretical puzzles.

Contribution

It analyzes the dynamical instability of small Schwarzschild-AdS black holes and explores their holographic implications in large-N gauge theories, highlighting differences between large N and thermodynamic limits.

Findings

Small Schwarzschild-AdS black holes become dynamically unstable.

The evolution relates to supercooled plasma in gauge theory.

Discussion of differences between large N limit and thermodynamic limit.

Abstract

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS$_5 \times S^5$ spacetime are known to become dynamically unstable toward deformation of the internal $S^5$ geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-$N$ Yang-Mills theory on $R \times S^3$. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large $N$ limit in the dual field theory and typical large volume thermodynamic limits.