Gauge Symmetry and Integrable Models

Abstract

We establish the isomorphism between a nonlinear $\sigma$-model and the abelian gauge theory on an arbitrary curved background, which allows us to derive integrable models and the corresponding Lax representations from gauge theoretical point of view. In our approach the spectral parameter is related to the global degree of freedom associated with the conformal or Galileo transformations of the spacetime. The B$\ddot{\mathrm{a}}$cklund transformations are derived from Chern-Simons theory where the spectral parameter is defined in terms of the extract compactified space dimension coordinate.

28 pages, no figures, latex

References in corpus (3)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Integrable Chern-Simons Gauge Field Theory in 2+1 Dimensions
• Chern-Simons Field Theory and Completely Integrable Systems