Statistical Mechanics of Vortices from D-branes and T-duality

TL;DR

This paper introduces a new method using D-branes and T-duality to compute the statistical mechanics of vortices in gauge theories, revealing differences in vortex 'softness' between Abelian and non-Abelian cases.

Contribution

It presents a novel approach to calculating vortex partition functions via D-brane realizations and T-duality, providing exact results and new insights into vortex interactions.

Findings

Results agree with exact moduli space integrations for Abelian-Higgs vortices.

The equation of state deviates from van der Waals, with the second virial coefficient scaling as 1/√N.

Non-Abelian vortices are found to be 'softer' than Abelian vortices.

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 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.