Isomonodromic properties of the Seiberg-Witten solution

Abstract

The Seiberg-Witten solution of N = 2 supersymmetric SU(2) gauge theories with matter is analyzed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on the moduli space while keeping their monodromies invariant. Well-known examples of isomonodromic sections are given by thev correlators of two-dimensional rational conformal field theories - the conformal blocks. The Seiberg-Witten section similarly admits the operations of braiding and fusing of its singularities, which obey the Yang-Bacter and Pentagonal identities, respectively. Using them, we easily find the complete expressions of the monodromies with affine team, and the full quantum numbers of the BPS spectrum. While the braiding describes the quark-monopole transmutation, the fusing implies the superconformal points in the moduli space. In the simplest case of three singularities, the supersymmetric sections are directly related to the conformal blocks of the logarithmic minimal models.