The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
arXiv:hep-th/9902205 · doi:10.1016/S0550-3213(99)00414-9
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, Ï(x_5 +R) = e^{2Ïiε}Ï(x_5), are imposed on half of the fields. This two-parameter (R,ε) 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.
18 pages, LaTeX