## Abstract

We study BPS states which arise in compactifications of M-theory on Calabi-Yau manifolds. In particular, we are interested in the spectrum of the particles obtained by wrapping M2-brane on a two-cycle in the CY manifold X. We compute the Euler characteristics of the moduli space of genus zero curves which land in a holomorphic four-cycle S ⊂ X. We use M. Kontsevich's method which reduces the problem to summing over trees and observe the discrepancy with the predictions of local mirror symmetry. We then turn this discrepancy into a supporting evidence in favor of existence of extra moduli of M2-branes which consists of the choice of a flat U(1) connection recently suggested by C. Vafa and partially confirm this by counting of the arbitrary genus curves of bi-degree (2, n) in ℙ^{1} × ℙ^{1} (this part has been done together with Barak Kol). We also make a conjecture concerning the counting of higher genus curves using second quantized Penner model and discuss possible applications to the string theory of two-dimensional QCD.

Original language | English |
---|---|

Pages (from-to) | XII-13 |

Journal | Journal of High Energy Physics |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

## Keywords

- M-Theory
- Nonperturbative Effects
- Sigma Models