1 research outputs found
Gauged vortices in a background
We discuss the statistical mechanics of a gas of gauged vortices in the
canonical formalism. At critical self-coupling, and for low temperatures, it
has been argued that the configuration space for vortex dynamics in each
topological class of the abelian Higgs model approximately truncates to a
finite-dimensional moduli space with a Kaehler structure. For the case where
the vortices live on a 2-sphere, we explain how localisation formulas on the
moduli spaces can be used to compute explicitly the partition function of the
vortex gas interacting with a background potential. The coefficients of this
analytic function provide geometrical data about the Kaehler structures, the
simplest of which being their symplectic volume (computed previously by Manton
using an alternative argument). We use the partition function to deduce simple
results on the thermodynamics of the vortex system; in particular, the average
height on the sphere is computed and provides an interesting effective picture
of the ground state.Comment: Final version: 22 pages, LaTeX, 1 eps figur