Large $N$ Topologically Twisted Indices, Holography, and Black Holes

Abstract

We present a simple closed form expression for the topologically twisted index of the ABJM theory as a function of the magnetic fluxes and complex chemical potentials valid at fixed $k$ and to all orders in the $1/N$ expansion. This in turn leads to analytic expressions for the topologically twisted index at fixed genus in the 't Hooft limit to all orders in the $1/\sqrt{\hat{I}}»$ expansion. These results have important implications for holography and the microscopic entropy counting of supersymmetric static AdS${}_4$ black holes. Generalizations to other SCFTs arising from M2-branes are also briefly discussed.

6 pages; v2: conjecture on the deformed 3-sphere partition function added, updated references; v3: minor typos corrected, version accepted for publication; v4: updated references