  The moduli space of SL(2) flat connections on a punctured Riemann surface
with the fixed conjugacy classes of the monodromies around the punctures is
endowed with a system of holomorphic Darboux coordinates, in which the
generating function of the variety of SL(2)-opers is identified with the
universal part of the effective twisted superpotential of the corresponding
four dimensional N=2 supersymmetric theory subject to the two-dimensional
Omega-deformation. This allows to give a definition of the Yang-Yang
functionals for the quantum Hitchin system in terms of the classical geometry
of the moduli space of local systems for the dual gauge group, and connect it
to the instanton counting of the four dimensional gauge theories, in the rank
one case.
