Conserved charges and supersymmetry in principal chiral models
Abstract
We consider local and non-local charges in bosonic and supersymmetric principal chiral models in 1+1 dimensions. In the bosonic case we point out that there exist local conserved charges, in involution with the Yangian non-local charges, which have spins equal to the orders of the Casimir operators and which therefore fit Dorey's construction. We clarify earlier arguments due to Goldschmidt and Witten which provide sufficient conditions for the quantum conservation of some of these local charges. As a prelude to the supersymmetric case, we analyze a general conservation equation in superspace and deduce that conserved charges in supersymmetric models need not have superpartners in general, but that superpartners may arise when the conserved current has a particular structure---a phenomenon illustrated by the partnership of energy-momentum and the supersymmetry charge itself. We then use a superfield formalism to discuss the local and non-local charges in the supersymmetric principal chiral model. Generalizing the Goldschmidt-Witten arguments, we show the existence of a higher (spin-5/2) conserved quantum supercurrent for the SU(N) case. We briefly discuss the implications for the multiplet structures in both the bosonic and supersymmetric theories.Keywords
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