Instability of supersymmetric black holes via quantum phase transitions

TL;DR

This paper demonstrates that certain four-dimensional hyperbolic supersymmetric black holes can become unstable in the canonical ensemble, suggesting a potential mechanism for supersymmetry breaking through quantum phase transitions.

Contribution

It introduces a broad class of $\,\mathcal{N}=2$ supergravity models and analyzes the stability of supersymmetric versus non-supersymmetric black holes within them.

Findings

Supersymmetric black holes can have higher free energy than non-supersymmetric ones.

Potential instability of supersymmetric solutions in specific parameter regimes.

Indication of a quantum phase transition leading to supersymmetry breaking.

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-Nordstr\"{o}m 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.