Wall-crossing, open BPS counting and matrix models

TL;DR

This paper explores wall-crossing phenomena in open BPS state counting related to D-branes in Calabi-Yau manifolds, connecting M-theory, topological strings, and matrix models with chamber dependence.

Contribution

It establishes a link between open BPS generating functions, topological string partition functions, and matrix model integrands, incorporating chamber dependence and geometric interpretation.

Findings

Open BPS generating functions are restrictions of open topological string partition functions.

These functions can be identified with matrix model integrands.

Chamber parameters have a natural geometric interpretation in crystal models.

Abstract

We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parameter specifying a choice of an open BPS chamber has a natural, geometric interpretation in the crystal model. These results extend previously known relations between open topological string amplitudes and matrix models to include chamber dependence.