From AdS3/CFT2 to Black Holes/Topological Strings

TL;DR

This paper demonstrates that the elliptic genus of certain 4D black holes can be approximated by the product of topological string partition functions, linking black hole entropy to topological string theory.

Contribution

It shows that the black hole partition function can be approximated by summing over membrane states, revealing a direct connection to topological string partition functions.

Findings

Membrane contributions yield the topological string partition function.

Antimembranes contribute the conjugate topological string partition function.

Black hole partition function approximates to the modulus squared of the topological string partition function.

Abstract

The elliptic genus Z_{BH} of a large class of 4D black holes can be expressed as an M-theory partition function on an AdS_3xS^2xCY_3 attractor. We approximate this partition function by summing over multiparticle chiral primary states of membranes which wrap curves in the CY_3 and tile Landau levels on the horizon S^2. Significantly, membranes and antimembranes can preserve the same supercharges if they occupy antipodal points on the horizon. It is shown the membrane contribution to Z_{BH} gives precisely the topological string partition function Z_{top} while the antimembranes give \bar Z_{top}, implying Z_{BH}=|Z_{top}|^2 in this approximation.