Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

TL;DR

This work investigates four-dimensional N=2 gauged supergravity with vector- and hypermultiplets and abelian gaugings of hypermultiplet isometries to study supersymmetric black holes and their attractors. It analytically constructs a magnetically charged BPS black hole in a minimal setting (one vector multiplet and the universal hypermultiplet), yielding a running dilaton and an interpolation from AdS2 x H2 near the horizon to a hyperscaling-violating geometry at infinity. A key contribution is the extension of the attractor mechanism to include hypermultiplets via an effective potential whose horizon values extremize all scalar fields and fix the entropy, recovering the ungauged limit in the appropriate case. The results provide analytical benchmarks for AdS/CFT and holographic condensed matter applications and lay groundwork for exploring more general gaugings and hypers.

Abstract

We consider four-dimensional $N=2$ supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic Kähler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ortín in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential ${\cal F}=-iχ^0χ^1$, 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.