### Abstract

We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vacuum expectation value of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the partition function gives a grand canonical ensemble of multi-instanton corrections for four-dimensional N=2 gauge theory in a suitable large N limit. We find two-dimensional gauge theories that provide the instanton partition function for four-dimensional N=2 theories with the hypermultiplets in the adjoint and fundamental representations. We also propose a partition function that gives the instanton contributions to four-dimensional N=2 quiver gauge theory. We discuss the relation between Nekrasov's instanton partition function and the Dijkgraaf-Vafa theory in terms of large N phase transitions of the generalized two-dimensional Yang-Mills theory.

Original language | English |
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Article number | 046006 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 73 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2006 Mar 2 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)