## Abstract

We test a recently proposed wall-crossing formula for the change of the Hilbert space of Bogomol'nyi-Prasad-Sommerfield (BPS) states in d = 4, N = 2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wall-crossing formula reproduces results of G̈ottsche and Yoshioka on wall-crossing behavior of the moduli of slope-stable holomorphic bundles over holomorphic surfaces. Our comparison shows very clearly that the moduli space of the D4D2D0 system on a rigid surface in a Calabi-Yau is not the same as the moduli space of torsion-free sheaves, even when worldhseet instantons are neglected. Moreover, we argue that the physical formula should make some new mathematical predictions for a future theory of the moduli of stable objects in the derived category.

Original language | English (US) |
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Pages (from-to) | 1621-1650 |

Number of pages | 30 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 14 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2010 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)