Quillen bundle and geometric prequantization of non-abelian vortices on a Riemann surface |
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Authors: | RUKMINI DEY SAMIR K PAUL |
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Institution: | 1.School of Mathematics,Harish Chandra Research Institute,Jhusi,India;2.S.N. Bose National Centre for Basic Sciences,Salt Lake,India |
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Abstract: | In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising
from 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 line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrized
by Ψ0, a section of a certain bundle. The equivalence of these prequantum bundles are discussed. |
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Keywords: | |
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