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- W3021373932 abstract "Non-perturbative aspects of $mathcal{N}=2$ supersymmetric gauge theories of class $mathcal{S}$ are deeply encoded in the algebra of functions on the moduli space $mathcal{M}_text{flat}$ of flat $SL(N)$-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on $mathcal{M}_text{flat}$. Via the decomposition of UV line operators into IR line operators, we determine their noncommutative algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein algebra studied in the context of Chern-Simons theory. Another realization of the skein algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class $mathcal{S}$ theories." @default.
- W3021373932 created "2020-05-13" @default.
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- W3021373932 date "2015-05-21" @default.
- W3021373932 modified "2023-10-01" @default.
- W3021373932 title "Line operators in theories of class $mathcal{S}$, quantized moduli space of flat connections, and Toda field theory" @default.
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