BPS black holes in AdS 4 from M-theory

Abstract

Abstract:We study supersymmetric black holes in AdS 4 in the framework of four dimensional gauged N = 2 supergravity coupled to hypermultiplets. We derive the flow equations for a general electrically gauged theory where the gauge group is Abelian and, restricting them to the fixed points, we derive the gauged supergravity analogue of the attractor equations for theories coupled to hypermultiplets. The particular models we analyze are consistent truncations of M-theory on certain Sasaki-Einstein seven-manifolds. We study the space of horizon solutions of the form AdS 2 × Σ g with both electric and magnetic charges and find a four-dimensional solution space when the theory arises from a reduction on Q 111 . For other SE 7 reductions, the solutions space is a subspace of this. We construct explicit examples of spherically symmetric black holes numerically.

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

“…Since our line of reasoning did not require the explicit solution beyond the AdS 4 boundary conditions, it should be straightforward to generalize these arguments to theories with charged hypermultiplets where solutions are harder to find [40][41][42][43][44][45] but there are more avenues for embedding such theories into string or M-theory. It would also seem likely that our methods will generalize to asymptotically AdS solutions in other dimensions.…”

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

“…The same formulation could possibly be generalized to the case with axions upon a suitable complexification of the equations, or to understand the string/M-theory origin of these black holes [38,49].…”

“…That was a gradient flow driven by the superpotential 49) however, since the BPS solution is just a particular case of the non-extremal set, it has to verify also a gradient flow driven by the magnetic superpotential W of eq. (3.25).…”

Betti multiplets, flows across dimensions and c-extremization

“…namely in our solutions, similarly to [42], the prepotentials are aligned in the σ 3 direction, namely P 3 I ≡ −i P I = 0. Moreover, this has the net effect of setting ω j µi = 0.…”

“…We conclude by computing c 2d and the structure of the mixing of the global currents of the 2d theory with the formalism developed above, matching the result with the one obtained in field theory. Let us finally mention that BPS solutions interpolating between an AdS 4 UV fixed point and AdS 2 , in theories with hypermultiplets and Betti multiplets have recently been found in [42].…”