A Farey Tail for Attractor Black Holes

TL;DR

This paper extends the Farey tail approach to attractor black holes in string theory, providing an exact asymptotic expansion of their microstate counting function via supergravity saddle points.

Contribution

It generalizes the Black Hole Farey Tail to attractor black holes using spectral flow and Rademacher formula, linking microscopic counts to supergravity solutions.

Findings

Exact asymptotic expansion of elliptic genus in terms of saddle points.

Generalization of the Farey Tail to attractor black holes.

Connection between microscopic counts and semi-classical supergravity.

Abstract

The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.