Gauged vortices in a background
@article{Romo2005GaugedVI, title={Gauged vortices in a background}, author={Nuno M. Rom{\~a}o}, journal={Journal of Physics A}, year={2005}, volume={38}, pages={9127-9144} }
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 Kahler 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…
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References
SHOWING 1-10 OF 27 REFERENCES
Dynamics of Abelian Higgs vortices in the near Bogomolny regime
- Physics, Mathematics
- 1994
The aim of this paper is to give an analytical discussion of the dynamics of the Abelian Higgs multi-vortices whose existence was proved by Taubes ([JT82]). For a particular value of a parameter of…
Quantum Chern–Simons vortices on a sphere
- Physics
- 2001
The quantization of the reduced first-order dynamics of the nonrelativistic model for Chern–Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric…
Asymptotic Interactions of Critically Coupled Vortices
- Physics, Mathematics
- 2003
Abstract: At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. Here, a formula for the asymptotic metric for two…
The dynamics of vortices on S2 near the Bradlow limit
- Mathematics
- 2003
The explicit solutions of the Bogomolny equations for N vortices on a sphere of radius R2>N are not known. In particular, this has prevented the use of the geodesic approximation to describe the low…
Volume of Vortex Moduli Spaces
- Physics
- 1999
Abstract:A gas of N Bogomol'nyi vortices in the Abelian Higgs model is studied on a compact Riemann surface of genus g and area A. The volume of the moduli space is computed and found to depend on N,…
Conservation laws in a first-order dynamical system of vortices
- Physics, Environmental Science
- 1999
The conservation laws for linear and angular momenta in a Schrodinger-Chern-Simons field theory modelling vortex dynamics in planar superconductors are studied. In analogy with fluid vortices it is…
Vortices in holomorphic line bundles over closed Kähler manifolds
- Mathematics
- 1990
We apply a modified Yang-Mills-Higgs functional to unitary bundles over closed Kähler manifolds and study the equations which govern the global minima. The solutions represent vortices in holomorphic…