KAC-MOODY ALGEBRA FOR TWO DIMENSIONAL PRINCIPAL CHIRAL MODELS

A Darboux transformation depending on single continuous parameter t is constructed for a principal chiral field. The transformation forms a nonlinear representation of the group for any fixed value of t. Part of the kernel in the Riemann-Hilbert transform is shown to be related to the Darboux transformation with its generators forming a Kac–Moody algebra. Conserved currents associated with the Kac–Moody algebra of the linearized equations and the Nöether current for the group transformations with fixed value of t are obtained.