BPS Microstates and the Open Topological String Wave Function

TL;DR

This paper proposes that the open topological string wave function encodes a grand canonical partition function for BPS black hole states bound to D-branes, extending the known closed string conjecture.

Contribution

It introduces a new conjecture linking open topological string wave functions to BPS black hole degeneracies, supported by a specific Type IIA Calabi-Yau example.

Findings

Verifies the conjecture in a local Calabi-Yau threefold case.

Connects BPS state degeneracies to q-deformed 2D Yang-Mills theory.

Supports the open string wave function as a BPS partition function.

Abstract

It has recently been conjectured that the closed topological string wave function computes a grand canonical partition function of BPS black hole states in 4 dimensions: Z_BH=|psi_top|^2. We conjecture that the open topological string wave function also computes a grand canonical partition function, which sums over black holes bound to BPS excitations on D-branes wrapping cycles of the internal Calabi-Yau: Z^open_BPS=|psi^open_top|^2. This conjecture is verified in the case of Type IIA on a local Calabi-Yau threefold involving a Riemann surface, where the degeneracies of BPS states can be computed in q-deformed 2-dimensional Yang-Mills theory.