Exact Black Hole Degeneracies and the Topological String

TL;DR

This paper computes the exact partition functions of BPS black holes in certain string theories, revealing their connection to topological string amplitudes and proposing a refined OSV conjecture to account for observed differences.

Contribution

It provides all-order perturbative calculations of black hole partition functions and introduces a modified OSV conjecture incorporating a measure factor.

Findings

Black hole partition functions match topological string amplitudes surprisingly well

Differences between black hole and topological string functions are explained by a measure factor

Results support a refined understanding of the OSV conjecture

Abstract

Motivated by the recent conjecture of Ooguri, Strominger and Vafa, we compute the semi-canonical partition function of BPS black holes in N=4 and N=8 string theories, to all orders in perturbation theory. Not only are the black hole partition functions surprisingly simple; they capture the full topological string amplitudes, as expected from the OSV conjecture. The agreement is not perfect, however, as there are differences between the black hole and topological string partition functions even at the perturbative level. We propose a minimal modification of the OSV conjecture, in which these differences are understood as a nontrivial measure factor for the topological string.