M-theory and a Topological String Duality

TL;DR

This paper explores the deep connection between topological string theory, BPS states in M-theory, and D-brane systems, providing evidence for a duality that links 4-dimensional and 5-dimensional black hole physics.

Contribution

It establishes a relation between topological string partition functions and D-brane systems via a topologically twisted gauge theory, supporting conjectures about DT invariants and black hole dualities.

Findings

Topological string partition functions relate to D-brane bound states.

The gauge theory description supports the DT invariants and topological string duality.

Evidence for the 4d/5d black hole connection is strengthened.

Abstract

We show how the topological string partition function, which is known to capture the degeneracies of a gas of BPS spinning M2-branes in M-theory compactified to 5 dimensions, is related to a 4-dimensional D-brane system that consists of single D6-brane bound to lower-dimensional branes. This system is described by a topologically twisted U(1) gauge theory, that has been conjecturally identified with quantum foam models and topological strings. This also explains, assuming the identification of Donaldson-Thomas invariants with this U(1) gauge theory, the conjectural relation between DT invariants and topological strings. Our results provide further mathematical evidence for the recently found connection between 4d and 5d black holes.