Black Hole Attractors and the Topological String

TL;DR

This paper proposes a conjecture linking the supersymmetric black hole partition function to the topological string partition function, providing evidence through perturbative expansion and connecting black hole microstates to topological string wavefunctions.

Contribution

It introduces a simple conjectural relationship between black hole and topological string partition functions and supports it with perturbative evidence.

Findings

Evidence for the conjecture in perturbation expansion

Black hole microstates related to topological string wavefunctions

Proposes a new perspective on BPS black hole entropy

Abstract

A simple relationship of the form Z_BH = |Z_top|^2 is conjectured, where Z_BH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Z_top is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.