  The analytic Langlands correspondence describes the solution to the spectral
problem for the quantised Hitchin Hamiltonians. It is related to the S-duality
of $\cal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation
of the Analytic Langlands Correspondence, and discuss its relations to quantum
field theory. The partition functions of the $H_3^+$ WZNW model are interpreted
as the wave-functions of a spherical vector in the quantisation of complex
Chern-Simons theory. Verlinde line operators generate a representation of two
copies of the quantised skein algebra on generalised partition functions. We
conjecture that this action generates a basis for the underlying Hilbert space,
and explain in which sense the resulting quantum theory represents a
deformation of the Analytic Langlands Correspondence.
