Isomonodromic deformations and supersymmetric gauge theories

Details Isomonodromic deformations and supersymmetric gauge theories Isomonodromic deformations and supersymmetric gauge theories

1996-03-12

arxiv.org/abs/hep-th/9603069v2

Int.J.Mod.Phys. A11 (1996) 5505-5518

Physics

High Energy Physics

High Energy Physics - Theory

Several typos are corrected, and a few sentenses are altered. 19 pp + a list of corrections (page 20), LaTeX

Scientific paper

10.1142/S0217751X96002522

Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isospectral problem), too, can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of $N=2$ SU($s$) supersymmetric Yang-Mills theory without matter is considered in detail for illustration. The isomonodromy problem in this case is closely related to the third Painlev\'e equation and its multicomponent analogues. An implicit relation to $t\tbar$ fusion of topological sigma models is thereby expected.

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