Twisted determinants on higher genus Riemann surfaces

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.

LaTeX, 26 pages,v3: typos corrected

References in corpus (1)

• Gauge/Gravity Correspondence from Open/Closed String Duality

Cited by in corpus (8)

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• The twisted open string partition function and Yukawa couplings
• Topological Masses From Broken Supersymmetry
• Multi-loop open string amplitudes and their field theory limit
• Two-loop Euler-Heisenberg effective actions from charged open strings
• Twisted determinants and bosonic open strings in an electromagnetic field
• Pinching parameters for open (super) strings
• Two-loop Yang-Mills diagrams from superstring amplitudes