Integrability and Seiberg-Witten Theory: Curves and Periods

TL;DR

This paper reviews how exact results in four-dimensional N=2 supersymmetric Yang-Mills theory relate to one-dimensional integrability, focusing on elliptic Calogero systems and their role in connecting N=4 and N=2 SUSY theories.

Contribution

It provides a detailed interpretation of low-energy exact results in N=2 SUSY YM using integrability theory, emphasizing the elliptic Calogero system.

Findings

Connection between Seiberg-Witten curves and integrable systems

Elliptic Calogero system models the flow between N=4 and N=2 SUSY

Insights into the structure of low-energy effective actions

Abstract

Interpretation of exact results on the low-energy limit of $4d$ $N=2$ SUSY YM in the language of $1d$ integrability theory is reviewed. The case of elliptic Calogero system, associated with the flow between $N=4$ and $N=2$ SUSY in $4d$, is considered in some detail.