Local Conserved Charges in Principal Chiral Models

We investigate local conserved charges in principal chiral models in 1+1 dimensions. There is a classically conserved local charge for each invariant tensor of the underlying group. We prove that these are always in involution with the non-local Yangian charges and we study their classical Poisson bracket algebra. For the groups U(N), O(N) and $Sp(N)$ we show that there are infinitely many commuting local charges, and we further identify finite sets of mutually commuting charges with spins equal to the Lie algebra exponents. We elaborate on arguments of Goldschmidt and Witten for conservation of some local charges at the quantum level, and we briefly discuss the implications for the multiplet structures. We comment on the possible existence of a version of Dorey's rule for the quantum principal chiral models.