Duality and black hole partition functions

TL;DR

This paper explores the connection between topological string partition functions and supersymmetric black hole entropy, proposing a modification to ensure compatibility with electric-magnetic duality in string theory contexts.

Contribution

It reviews the conjectured link between topological string and black hole partition functions and introduces a modification to align with electric-magnetic duality principles.

Findings

Proposes a modified partition function compatible with duality

Reviews the connection between topological strings and black hole entropy

Highlights the importance of duality in quantum gravity models

Abstract

Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of ten-dimensional string theory or eleven-dimensional M-theory, one has a microscopic description of the black hole which allows one to count microstates and to compare the result to the macroscopic (geometrical) entropy. Recently it has been conjectured that there is a very direct connection between the partition function of the topological string and a partition function for supersymmetric black holes. We review this idea and propose a modification which makes it compatible with electric-magnetic duality.