Quantum Statistical Mechanics of Vortices

TL;DR

This paper derives the high-temperature partition function and equation of state for quantized Abelian Higgs vortices, incorporating quantum corrections by analyzing the moduli space geometry.

Contribution

It introduces a method to compute the vortex gas partition function using the moduli space volume and curvature, including quantum effects.

Findings

Partition function computed at high temperature with quantum corrections

Equation of state derived for vortex gas

Moduli space geometry used to evaluate quantum effects

Abstract

The asymptotic partition function for quantized Abelian Higgs vortices at high temperature $T$ is found to leading and subleading order, and from this the equation of state of the vortex gas is derived, including the first quantum correction. It is assumed that the Hamiltonian is proportional to the Laplace--Beltrami operator on the moduli space of static $N$-vortex solutions. The partition function is calculated using the total volume and total scalar curvature of the moduli space.