Instability of supersymmetric black holes via quantum phase transitions

Abstract

In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\mathcal{N}=2$ supergravity theories interpolating between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\mathcal{N}=8$ supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable choices of the parameters defining the $\mathcal{N}=2$ model, the supersymmetric solution features a higher free energy than the non-supersymmetric one. In the absence of additional selection rules, this would imply an instability of the supersymmetric configuration, hinting towards a possible supersymmetry breaking mechanism.

arXiv comment14 pages

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