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arXiv · hep-th/0306129

Twisted determinants on higher genus Riemann surfaces

Rodolfo Russo·Stefano Sciuto
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Abstract

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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Rodolfo Russo, Stefano Sciuto. 2007-09-12. Twisted determinants on higher genus Riemann surfaces. https://doi.org/10.1016/j.nuclphysb.2003.07.016

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