Supersymmetric black holes in AdS4 from very special geometry

Abstract

Supersymmetric black holes in AdS spacetime are inherently interesting for the AdS/CFT correspondence. Within a four dimensional gauged supergravity theory coupled to vector multiplets, the only analytic solutions for regular, supersymmetric, static black holes in AdS 4 are those in the STU-model due to Cacciatori and Klemm. We study a class of U (1)-gauged supergravity theories coupled to vector multiplets which have a cubic prepotential, the scalar manifold is then a very special Kähler manifold. When the resulting very special Kähler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS 4 black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus.

On the on-shell: the action of AdS4 black holes

“…Starting from [3], the solution for BPS black holes in AdS 4 has been developed [19][20][21][22] and in [7] a general solution for dyonically charged, AdS 4 black holes in FI-gauged supergravity (with general dyonic gaugings) was derived. This solution assumes that M v is a homogeneous space and is presented in terms of the quartic invariant 7 I 4 .…”

“…To continue this final step, we first assume that the scalar fields z i are purely imaginary (in the conventions of [21]). Such solutions might be called magnetic black holes since in the duality frame of [3,21], the charges of the black holes are purely magnetic.…”

“…Such solutions might be called magnetic black holes since in the duality frame of [3,21], the charges of the black holes are purely magnetic. We wish to enforce Neumann boundary conditions on the resulting imaginary scalar fields, as is well known [14]: we should perform a Legendre transform…”

“…This includes the class of black holes in [3,21] as well as those related by duality transformation [28,39].…”

First order flow for non-extremal AdS black holes and mass from holographic renormalization

“…where the hatted tensor is a constant tensor satisfyingd ijk d j(lm d np)k = 64 27 δ i (l d mnp) [37]. All very special geometries descend from a 5-dimensional N = 2 theory coupled to n V − 1 vector multiplets.…”