Integrability and Seiberg-Witten exact solution

The exact Seiberg-Witten (SW) description of the light sector in the N = 2 SUSY 4d Yang-Mills theory [N. Seiberg and E. Witten, Nucl. Phys. B 430 (1994) 485 (E); B 446 (1994) 19] is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) [A. Gurevich and L. Pitaevsky, JETP 65 (1973) 65; see also, S. Novikov, S. Manakov, L. Pitaevsky and V. Zakharov, Theory of solitons] solution to the elliptic Whitham equations. We consider this as an implication that the dynamical mechanism behind the SW solution is related to integrable systems on the moduli space of instantons. We emphasize the role of the Whitham theory as a possible substitute of the renormalization-group approach to the construction of low-energy effective actions.