### Abstract

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit q →exp(2Πi/k) of the q-deformed partition function plays a crucial role in the orbifold projection while the limit q → 1 applies to R4. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

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

Article number | 015 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- M(atrix) Theories
- Matrix Models
- Supersymmetric gauge theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Matrix model from N = 2 orbifold partition function.** / Kimura, Taro.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2011, no. 9, 015. https://doi.org/10.1007/JHEP09(2011)015

}

TY - JOUR

T1 - Matrix model from N = 2 orbifold partition function

AU - Kimura, Taro

PY - 2011

Y1 - 2011

N2 - The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit q →exp(2Πi/k) of the q-deformed partition function plays a crucial role in the orbifold projection while the limit q → 1 applies to R4. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

AB - The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit q →exp(2Πi/k) of the q-deformed partition function plays a crucial role in the orbifold projection while the limit q → 1 applies to R4. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

KW - M(atrix) Theories

KW - Matrix Models

KW - Supersymmetric gauge theory

UR - http://www.scopus.com/inward/record.url?scp=80053202832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053202832&partnerID=8YFLogxK

U2 - 10.1007/JHEP09(2011)015

DO - 10.1007/JHEP09(2011)015

M3 - Article

VL - 2011

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 015

ER -