Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-22
Nucl.Phys.B788:120-136,2008
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, 18 figures
Scientific paper
10.1016/j.nuclphysb.2007.06.020
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 there 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.
Eto Minoru
Fujimori Toshiaki
Nitta Muneto
Ohashi Keisuke
Ohta Kazutoshi
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