This paper addresses a long standing problem, the counting of the microstates of supersymmetric asymptotically AdS black holes in terms of a holographically dual field theory. We focus on a class of asymptotically AdS₄ static black holes preserving two real supercharges which are dual to a topologically twisted deformation of the ABJM theory. We evaluate in the large N limit the topologically twisted index of the ABJM theory and we show that it correctly reproduces the entropy of the AdS₄ black holes. An extremization of the index with respect to a set of chemical potentials is required. We interpret it as the selection of the exact R-symmetry of the superconformal quantum mechanics describing the horizon of the black hole.

We present a counting of microstates of a class of dyonic BPS black holes in AdS$_4$ which precisely reproduces their Bekenstein-Hawking entropy. The counting is performed in the dual boundary description, that provides a non-perturbative definition of quantum gravity, in terms of a twisted and mass-deformed ABJM theory. We evaluate its twisted index and propose an extremization principle to extract the entropy, which reproduces the attractor mechanism in gauged supergravity.Comment: 4 page

We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS₅ × S⁵ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for \( \mathcal{N}=4 \) super Yang-Mills.

We elaborate further on the static supersymmetric AdS₄ black holes found in [1], investigating thoroughly the BPS constraints for spherical symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos terms. We find Killing spinors that preserve two of the original eight supercharges and investigate the conditions for genuine black holes free of naked singularities. The existence of a horizon is intimately related with the requirement that the scalars are not constant, but given in terms of harmonic functions in analogy to the attractor flow in ungauged supergravity. The black hole charges depend on the choice of the electromagnetic gauging, with only magnetic charges for purely electric gaugings. Finally we show how these black holes can be embedded in N = 8 supergravity and thus in M-theory.

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS₄ × S⁶ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional \( \mathcal{N}=2 \) Chern-Simons-matter gauge theories in the large N limit. The I-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic \( \mathcal{N}=2 \) gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on S⁶. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.

We present new results towards the construction of the most general black hole solutions in four-dimensional Fayet-Iliopoulos gauged supergravities. In these theories black holes can be asymptotically AdS and have arbitrary mass, angular momentum, electric and magnetic charges and NUT charge. Furthermore, a wide range of horizon topologies is allowed (compact and noncompact) and the complex scalar fields have a non-trivial radial and angular profile. We construct a large class of solutions in the simplest single scalar model with prepotential F = −iX ⁰ X ¹ and discuss their thermodynamics. Moreover, various approaches and calculational tools for facing this problem with more general prepotentials are presented.