### 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 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

**Localization on the D-brane, two-dimensional gauge theory and matrix models.** / Matsuura, So; Ohta, Kazutoshi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Localization on the D-brane, two-dimensional gauge theory and matrix models

AU - Matsuura, So

AU - Ohta, Kazutoshi

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33344479247&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.73.046006

DO - 10.1103/PhysRevD.73.046006

M3 - Article

AN - SCOPUS:33344479247

VL - 73

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 4

M1 - 046006

ER -