Integrability and Seiberg-Witten Exact Solution

TL;DR

This paper explores the connection between Seiberg-Witten solutions in N=2 SUSY Yang-Mills theory and integrable systems, proposing that the low-energy dynamics can be understood through elliptic Whitham equations and integrable models.

Contribution

It reformulates the Seiberg-Witten solution in terms of integrable systems and suggests Whitham theory as an alternative to renormalization-group methods for effective action construction.

Findings

Seiberg-Witten solutions relate to Gurevich-Pitaevsky solutions of elliptic Whitham equations.

The dynamical mechanism behind SW solutions is linked to integrable systems on instanton moduli space.

Whitham theory may serve as a substitute for renormalization-group approaches in low-energy effective theories.

Abstract

The exact Seiberg-Witten (SW) description of the light sector in the $N=2$ SUSY $4d$ Yang-Mills theory is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) solution to the elliptic Whitham equations. We consider this as an implication that 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.