### Abstract

We examine the two-dimensional U(N) Yang-Mills theory by using the technique of random partitions. We show that the large N limit of the partition function of the 2D Yang-Mills theory on S^{2} reproduces the instanton counting of 4D N = 2 supersymmetric gauge theories introduced by Nekrasov. We also discuss that we can take the "double scaling limit" by fixing the product of the N and cell size in Young diagrams, and the effective action given by Douglas and Kazakov is naturally obtained by taking this limit. We give an interpretation for our result from the view point of the superstring theory by considering a brane configuration that realizes 4D N = 2 supersymmetric gauge theories.

Original language | English |
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Pages (from-to) | 643-660 |

Number of pages | 18 |

Journal | Journal of High Energy Physics |

Issue number | 3 |

Publication status | Published - 2005 Mar 1 |

Externally published | Yes |

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### Keywords

- Field Theories in Lower Dimensions
- Solitons Monopoles and Instantons
- Supersymmetric Effective Theories

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*, (3), 643-660.