### 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 |
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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