Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

TL;DR

This paper constructs a new supersymmetric black hole solution in gauged supergravity with hypermultiplets, revealing a flow from AdS2×H2 to a hyperscaling-violating geometry, and extends attractor analysis to include hypermultiplet scalars.

Contribution

It provides an explicit supersymmetric black hole solution with hypermultiplets and extends attractor mechanism analysis to theories with hypermultiplets present.

Findings

Black hole solution with running dilaton interpolates between AdS2×H2 and hyperscaling-violating geometry.

Magnetic charges are fixed by the gauging parameters.

Attractors are governed by an effective potential whose extremum determines scalar values and entropy.

Abstract

We consider four-dimensional $N=2$ supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic K\"ahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ort\'{\i}n in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential ${\cal F}=-i\chi^0\chi^1$, and the universal hypermultiplet. This solution has a running dilaton, and it interpolates between $\text{AdS}_2\times\text{H}^2$ at the horizon and a hyperscaling-violating type geometry at infinity, conformal to $\text{AdS}_2\times\text{H}^2$. It carries two magnetic charges that are completely fixed in terms of the parameters that appear in the Killing vector used for the gauging. In the second part of the paper, we extend the work of Bellucci et al. on black hole attractors in gauged supergravity to the case where also hypermultiplets are present. The attractors are shown to be governed by an effective potential $V_{\text{eff}}$, which is extremized on the horizon by all the scalar fields of the theory. Moreover, the entropy is given by the critical value of $V_{\text{eff}}$. In the limit of vanishing scalar potential, $V_{\text{eff}}$ reduces (up to a prefactor) to the usual black hole potential.