The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory

TL;DR

This paper explores the connection between the elliptic Ruijsenaars-Schneider integrable system and four-dimensional N=2 supersymmetric Yang-Mills theories derived from five-dimensional models through compactification and boundary conditions.

Contribution

It establishes the Ruijsenaars-Schneider model as the integrable system associated with a broad class of N=2 SUSY YM theories obtained via specific compactifications.

Findings

The elliptic Ruijsenaars-Schneider model corresponds to these compactified theories.

Weak coupling limit is described by the trigonometric Ruijsenaars-Schneider model.

The study links supersymmetric gauge theories with integrable systems.

Abstract

The compactification of five dimensional N=2 SUSY Yang-Mills (YM) theory onto a circle provides a four dimensional YM model with N=4 SUSY. This supersymmetry can be broken down to N=2 if non-trivial boundary conditions in the compact dimension, \phi(x_5 +R) = e^{2\pi i\epsilon}\phi(x_5), are imposed on half of the fields. This two-parameter (R,\epsilon) family of compactifications includes as particular limits most of the previously studied four dimensional N=2 SUSY YM models with supermultiplets in the adjoint representation of the gauge group. The finite-dimensional integrable system associated to these theories via the Seiberg-Witten construction is the generic elliptic Ruijsenaars-Schneider model. In particular the perturbative (weak coupling) limit is described by the trigonometric Ruijsenaars-Schneider model.