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 $$ \mathcal{N} $$ N = 2 supergravity theories interpolating between all the single dilaton truncations of the SO(8) gauged $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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.

Solitons as ground states in supergravity theories

“…This last situation only occurs for values of the charges at infinity for which the free energy of the susy solution is lower than the non-supersymmetric one, as one naively expects [9]. Then, there is no conflict with the prescriptions of the positive energy theorem and the presented scenario is of interest, as an example of framework in which an instability under quantum phase transitions can occur [27].…”

Supersymmetric solitons in gauged $$ \mathcal{N} $$ = 8 supergravity

“…It is also possible to construct black holes in this theory [17][18][19][20][21][22][23] and endow them with Wilson lines along the lines of [24]. This will provide an even more complete phase diagram of this model that we leave to analyze in the future.…”