  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.
