Nonlocal conserved currents for two-dimensional chiral theories

We derive an infinite set of conserved nonlocal currents for two-dimensional chiral models with fields assuming values in an arbitrary Lie group G. Explicit formulas are presented for the Minkowski metric, but with slight changes described in the text the analogous results are valid for the Euclidean case as well. The Poisson-bracket algebra of conserved charges is further analyzed for G = SU(2). We expose the geometric structure of chiral models, and outline the relation between models described in this paper and chiral theories corresponding to lower-dimensional homogeneous spaces