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 / N , implying that non-Abelian vortices are “softer” than Abelian vortices. Vortices on a sphere are also briefly discussed.
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