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Line operators on S^1xR^3 and quantization of the Hitchin moduli space

We perform an exact localization calculation for the expectation values of Wilson-'t Hooft line operators in N=2 gauge theories on S^1xR^3. The expectation values are naturally expressed in terms of the complexified Fenchel-Nielsen coordinates, and form a quantum mechanically deformed algebra of functions on the associated Hitchin moduli space by Moyal multiplication. We propose that these expectation values are the Weyl transform of the Verlinde operators, which act on Liouville/Toda conformal blocks as difference operators. We demonstrate our proposal explicitly in SU(N) examples.

preprint2016arXivOpen access
Yuto ItoTakuya OkudaMasato Taki
hep-th
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Yuto ItoTakuya OkudaMasato Taki

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