Mathematical Physics Seminar
Monday 30.XI.2009
Time: 16:00-17:00
Room: 0089
Instytut Matematyki, ul. Łojasiewicza 6, 30-348 Kraków
Nuno Romão
(Uniwersytet Jagielloński, Cracow, Poland)
Gauged vortices and localisation II
Abstract:
The vortex equations describe field configurations in a U(1) gauge theory on a
Riemann surface Σ. Their moduli spaces support natural Kähler structures,
defined in terms of integrals of field configurations over Σ. In this second talk
(of a series of two), I will focus on the case where Σ is a round 2-sphere, for
which one can make use of some symplectic techniques to study the geometry
of the moduli spaces (which are then complex projective spaces). On each moduli
space there is an SO(3)-moment map, and the study of the cicle actions corresponding
to any of its components allows one to calculate (via Duistermaat-Heckman
localisation) certain integrals in terms of information around the set of critical points.
I will try to motivate these quantities from a physical perspective, and give an
application to the calculation of a partition function in classical statistical mechanics,
describing a gas of vortices moving on a 2-sphere with a natural potential.
Reference:
N.M. Romão: "Gauged vortices in a background", arXiv:
hep-th/0503014
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