GAUGE SYMMETRY AND INTEGRABLE MODELS

SHAO-SHIUNG LIN OKTAY K. PASHAEV AND SHI-SHYR ROAN

Abstract. We establish the isomorphism between a nonlinear σ-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 Bäcklund transformations are derived from Chern-Simons theory where the spectral parameter is defined in terms of the extract compactified space dimension coordinate.