Nuno M Romão 2005 J. Phys. A: Math. Gen. 38 9127 doi:10.1088/0305-4470/38/41/020
Gauged vortices in a background
Nuno M Romão
Show affiliationsWe 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 Kähler structure. For the case where the vortices live on a 2-sphere, we explain how localization formulae on the moduli spaces can be used to compute exactly the partition function of the vortex gas interacting with a background potential. The coefficients of this analytic function provide geometrical data about the Kähler 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.
- PACS
- MSC
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81T45 Topological field theories (See also 57R56, 58Dxx)
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
- Subjects
- Dates
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Issue 41 (14 October 2005)
Received 7 March 2005, in final form 29 August 2005
Published 28 September 2005
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Gauged vortices in a background
Nuno M Romão 2005 J. Phys. A: Math. Gen. 38 9127
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