2 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
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.