Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface

Details Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface

2010-12-21

arxiv.org/abs/1012.4616v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from the $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen's determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct Quillen line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrised by $\Psi_0$, a section of a certain bundle.

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