AdS4 black holes from M-theory

TL;DR

This paper derives flow equations for AdS4 black holes from eleven-dimensional supergravity, establishing a link with four-dimensional gauged supergravity models through K"ahler manifold reductions.

Contribution

It formulates BPS conditions as polyform equations on K"ahler manifolds, connecting eleven-dimensional supergravity to four-dimensional gauged supergravity.

Findings

Flow equations match those of known gauged supergravity models.

Potential to derive gauged supergravities from K"ahler manifold reductions.

Provides a framework for exploring new consistent truncations.

Abstract

We consider the BPS conditions of eleven dimensional supergravity, restricted to an appropriate ansatz for black holes in four non-compact directions. Assuming the internal directions to be described by a circle fibration over a K\"ahler manifold and considering the case where the complex structure moduli are frozen, we recast the resulting flow equations in terms of polyforms on this manifold. The result is a set of equations that are in direct correspondence with those of gauged supergravity models in four dimensions consistent with our simplifying assumptions. In view of this correspondence even for internal manifolds that do not correspond to known consistent truncations, we comment on the possibility of obtaining gauged supergravities from reductions on K\"ahler manifolds.