Localised $\mathbf{Ad}{\mathbf{S}}_5\times {\mathbf{S}}^5$ Black Holes

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.

11 pages, 6 figures

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