  We will propose a derivation of the correspondence between certain gauge
theories with N=2 supersymmetry and conformal field theory discovered by Alday,
Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain
results from the literature we argue that the quantum theory of the moduli
spaces of flat SL(2,R)-connections represents a non-perturbative "skeleton" of
the gauge theory, protected by supersymmetry. It follows that instanton
partition functions can be characterized as solutions to a Riemann-Hilbert type
problem. In order to solve it, we describe the quantization of the moduli
spaces of flat connections explicitly in terms of two natural sets of Darboux
coordinates. The kernel describing the relation between the two pictures
represents the solution to the Riemann Hilbert problem, and is naturally
identified with the Liouville conformal blocks.
