Comments on deconfinement in AdS/CFT

TL;DR

This paper investigates the deconfinement phase transition in the index of $ ext{N}=4$ Yang-Mills theory on $S^3 imes ext{R}$, proposing an upper bound related to a Hagedorn-like temperature and suggesting new black hole solutions in AdS$_5$.

Contribution

It introduces an upper bound on the deconfinement temperature in the theory by optimizing fugacity phases, indicating potential new black hole states below known Hawking-Page transition temperatures.

Findings

Derived an upper bound on the deconfinement temperature.

Found the bound has features similar to the Hagedorn temperature.

Suggests existence of new black holes in AdS$_5$.

Abstract

We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$. We argue that the index should undergo a large $N$ deconfinement phase transition, by computing an upper bound of its `temperature.' We compute this bound by optimizing the phases of fugacities. The bound we find has some features analogous to the Hagedorn temperature. We briefly discuss a possible mechanism of the actual deconfinement transition below our bound. Our upper bound is lower than the Hawking-Page transition `temperature' of known BPS black holes in the AdS$_5$ dual. We thus expect the existence of new black holes.