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