A Universal Counting of Black Hole Microstates in AdS${}_4$

Abstract

Many three-dimensional $\mathcal{N}=2$ SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS${}_4$ magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS${}_2$ solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

31 pages + appendices; v2: Added a discussion on the relation between black hole entropy and the on-shell action. Additional references