Quantum Statistical Mechanics of Vortices

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.