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arXiv · 1805.10992

Quantum Wilson surfaces and topological interactions

Olga Chekeres
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Abstract

We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal $G$-bundle $P \to Σ$. Interestingly, it can interact topologically with 2-dimensional Yang-Mills and BF theories modifying their partition functions. We compute explicitly the partition function of the 2-dimensional Yang-Mills theory with a Wilson surface. The Wilson surface turns out to be nontrivial for the gauge group $G$ non-simply connected (and trivial for $G$ simply connected). In particular we study in detail the cases $G=SU(N)/\mathbb{Z}_m$, $G=Spin(4l)/(\mathbb{Z}_2\oplus\mathbb{Z}_2)$ and obtain a general formula for any compact connected Lie group.

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Olga Chekeres. 2018-05-28. Quantum Wilson surfaces and topological interactions. https://doi.org/10.1007/jhep02(2019)030

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