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Wilson surface observables from equivariant cohomology

Mnev, Pavel
Published in Journal of High Energy Physics. 2015, vol. 1511, p. 093-115
Collection Open Access - SCOAP3
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).
Keywords Wilson’t Hooft and Polyakov loopsDifferential and Algebraic GeometrySigma ModelsGauge Symmetry
arXiv: 1507.06343
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ALEXEEV, Anton, CHEKERES, Olga, MNEV, Pavel. Wilson surface observables from equivariant cohomology. In: Journal of High Energy Physics, 2015, vol. 1511, p. 093-115. doi: 10.1007/JHEP11(2015)093 https://archive-ouverte.unige.ch/unige:78170

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Deposited on : 2015-12-03

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