## Abstract

We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y ^{p,q} manifolds and give rise via M-theory compactification to SU(p) gauge theories on ℝ^{4}× S^{1}. As an application we present a detailed study of the local F_{2}case and compute open and closed genus zero Gromov-Witten invariants of the bC_{3}Z_{4} orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes. The mirror curve in this case is the spectral curve of the relativistic A _{1} Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y ^{p,q} geometries.

Original language | English |
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Pages (from-to) | 205-252 |

Number of pages | 48 |

Journal | Communications in Mathematical Physics |

Volume | 289 |

Issue number | 1 |

Early online date | 24 Apr 2009 |

DOIs | |

Publication status | Published - 1 Jul 2009 |

## Keywords

- Gauge Theory
- Modulus Space
- Modular Form
- Topological String
- Toda Chain

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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