Exact and Asymptotic Degeneracies of Small Black Holes

TL;DR

This paper investigates the relationship between black hole entropy and topological string theory, showing that for certain supersymmetric models, macroscopic and microscopic degeneracies match perturbatively but differ non-perturbatively.

Contribution

It refines existing proposals on black hole degeneracies by analyzing specific N=4 and N=2 models and clarifies the domain of validity of these relations.

Findings

Macroscopic degeneracy matches microscopic to all orders in perturbation theory.

Non-perturbative corrections are computable on the heterotic side.

Refined understanding of the role of helicity supertraces.

Abstract

We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N=4 and N=2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but misses non-perturbative corrections which are computable on the heterotic side. Using these examples we refine the previous proposals and comment on their domain of validity as well as on the relevance of helicity supertraces.