Integrable Structures in Supersymmetric Gauge and String Theory

TL;DR

This paper reveals that the effective action of N=2 supersymmetric Yang-Mills theory with matter is described by an integrable spin model on an elliptic curve, connecting gauge theory, integrable systems, and string theory.

Contribution

It demonstrates the integrable spin model structure underlying N=2 Yang-Mills theories and suggests extensions to broader models and string theory.

Findings

Effective action governed by an elliptic integrable spin model

Route to derive dynamics from Yang-Mills theory outlined

Potential generalizations to all N=2 models and string theory proposed

Abstract

The effective action of N=2 Yang-Mills theory with adjoint matter is shown to be governed by an integrable spin model with spectral parameter on an elliptic curve. We sketch a route to deriving this effective dynamics from the underlying Yang-Mills theory. Natural generalizations of this structure to all N=2 models, and to string theory, are suggested.