# Abelian Yang-Mills theory on real tori and theta divisors of Klein surfaces

Okonek, Christian; Teleman, Andrei (2013). Abelian Yang-Mills theory on real tori and theta divisors of Klein surfaces. Communications in Mathematical Physics, 323(3):813-858.

## Abstract

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.

## Abstract

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Statistical and Nonlinear Physics Physical Sciences > Mathematical Physics English September 2013 27 Dec 2013 12:48 30 Jul 2020 11:06 Springer 0010-3616 Closed Publisher DOI. An embargo period may apply. https://doi.org/10.1007/s00220-013-1793-z