Wall crossing in local Calabi Yau manifolds

TL;DR

This paper investigates BPS states in a D-brane system on the conifold, revealing the need for an extra parameter in BPS counting and illustrating limitations of supergravity methods in wall-crossing phenomena.

Contribution

It introduces an additional real parameter for BPS partition functions in conifold setups and connects supergravity results with Donaldson-Thomas theory, highlighting approach limitations.

Findings

Extra real parameter needed for BPS counting

Supergravity approach reproduces Donaldson-Thomas results

Identifies limitations of supergravity in wall-crossing analysis

Abstract

We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kahler parameter of the rigid sphere it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability walls. The supergravity approach to BPS state-counting gives a simple derivation of results of Szendroi concerning Donaldson-Thomas theory on the noncommutative conifold. This example also illustrates some interesting limitations on the supergravity approach to BPS state-counting and wall-crossing.