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

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 spec...

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Bibliographic Details
Published in:Nuclear physics. B 2008-01, Vol.788 (3), p.120-136
Main Authors: Eto, Minoru, Fujimori, Toshiaki, Nitta, Muneto, Ohashi, Keisuke, Ohta, Kazutoshi, Sakai, Norisuke
Format: Article
Language:English
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Summary: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 / N , implying that non-Abelian vortices are “softer” than Abelian vortices. Vortices on a sphere are also briefly discussed.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2007.06.020