Twisted determinants on higher genus Riemann surfaces

Details Twisted determinants on higher genus Riemann surfaces Twisted determinants on higher genus Riemann surfaces

2003-06-13

arxiv.org/abs/hep-th/0306129v3

Nucl.Phys. B669 (2003) 207-232

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 26 pages,v3: typos corrected

Scientific paper

10.1016/j.nuclphysb.2003.07.016

We study the Dirac and the Laplacian operators on orientable Riemann surfaces of arbitrary genus g. In particular we compute their determinants with twisted boundary conditions along the b-cycles. All the ingredients of the final results (including the normalizations) are explicitly written in terms of the Schottky parametrization of the Riemann surface. By using the bosonization equivalence, we derive a multi-loop generalization of the well-known g=1 product formulae for the Theta-functions. We finally comment on the applications of these results to the perturbative theory of open charged strings.

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