Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-10-31
Nucl.Phys. B524 (1998) 469-501
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 40 pages, 9 eps figures. Correction of misprints only
Scientific paper
10.1016/S0550-3213(98)00245-4
The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed 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 the 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-Baxter and Pentagonal identities, respectively. Using them, we easily find the complete expressions of the monodromies with affine term, 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.
Cappelli Andrea
Valtancoli Paolo
Vergnano Luca
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