### Abstract

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U (N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / sqrt(N), implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

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

Pages (from-to) | 120-136 |

Number of pages | 17 |

Journal | Nuclear Physics B |

Volume | 788 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 Jan 14 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*788*(3), 120-136. https://doi.org/10.1016/j.nuclphysb.2007.06.020

**Statistical mechanics of vortices from D-branes and T-duality.** / Eto, Minoru; Fujimori, Toshiaki; Nitta, Muneto; Ohashi, Keisuke; Ohta, Kazutoshi; Sakai, Norisuke.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 788, no. 3, pp. 120-136. https://doi.org/10.1016/j.nuclphysb.2007.06.020

}

TY - JOUR

T1 - Statistical mechanics of vortices from D-branes and T-duality

AU - Eto, Minoru

AU - Fujimori, Toshiaki

AU - Nitta, Muneto

AU - Ohashi, Keisuke

AU - Ohta, Kazutoshi

AU - Sakai, Norisuke

PY - 2008/1/14

Y1 - 2008/1/14

N2 - We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U (N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / sqrt(N), implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

AB - We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U (N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / sqrt(N), implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=35648979116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35648979116&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2007.06.020

DO - 10.1016/j.nuclphysb.2007.06.020

M3 - Article

AN - SCOPUS:35648979116

VL - 788

SP - 120

EP - 136

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -