Seiberg-Witten theories and AGT relations
Exact results in N=2 supersymmetric gauge theories are based on geometric definition of the Seiberg-Witten prepotentials. Their deformed version - Nekrasov partition functions can be defined purely in terms of 2D conformal field theory. In the simplest cases this goes back to the fermionic representations of tau-functions, and now becomes clearly related to the isomonodromic deformation problems.
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