Localised $\bf{AdS_5\times S^5}$ Black Holes

TL;DR

This paper constructs localized AdS_5 x S^5 black holes numerically, revealing a phase transition linked to symmetry breaking in the dual super Yang-Mills theory.

Contribution

It provides the first numerical solutions of localized AdS_5 x S^5 black holes and analyzes their phase transition and dual field theory implications.

Findings

Identified a first-order phase transition at higher energies.

Computed scalar operator expectation values in the low energy phase.

Extrapolated the phase transition point in the parameter space.

Abstract

We numerically construct asymptotically global $\mathrm{AdS}_5\times \mathrm{S}^5$ black holes that are localised on the $\mathrm{S}^5$. These are solutions to type IIB supergravity with $\mathrm S^8$ horizon topology that dominate the theory in the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to $\mathrm{AdS}_5$-Schwarzschild$\times \mathrm{S}^5$. By the AdS/CFT correspondence, this transition is dual to spontaneously breaking the $SO(6)$ R-symmetry of $\mathcal N=4$ super Yang-Mills down to $SO(5)$. We extrapolate the location of this phase transition and compute the expectation value of the resulting scalar operators in the low energy phase.