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arXiv · 1507.06343

Wilson surface observables from equivariant cohomology

Anton Alekseev·Olga Chekeres·Pavel Mnev
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Abstract

Wilson lines in gauge theories admit several path integral descriptions. The first one (due to Alekseev-Faddeev-Shatashvili) uses path integrals over coadjoint orbits. The second one (due to Diakonov-Petrov) replaces a 1-dimensional path integral with a 2-dimensional topological $σ$-model. We show that this $σ$-model is defined by the equivariant extension of the Kirillov symplectic form on the coadjoint orbit. This allows to define the corresponding observable on arbitrary 2-dimensional surfaces, including closed surfaces. We give a new path integral presentation of Wilson lines in terms of Poisson $σ$-models, and we test this presentation in the framework of the 2-dimensional Yang-Mills theory. On a closed surface, our Wilson surface observable turns out to be nontrivial for $G$ non-simply connected (and trivial for $G$ simply connected), in particular we study in detail the cases $G=U(1)$ and $G=SO(3)$.

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Anton Alekseev, Olga Chekeres, Pavel Mnev. 2015-09-23. Wilson surface observables from equivariant cohomology. https://doi.org/10.1007/jhep11(2015)093

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