Yangian superalgebras in conformal field theory

Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main examples are sigma models of the supergroups PSL(N vertical bar N), OSP(2N + 2 vertical bar 2N) and D(2, 1; alpha) away from the WZW point. Further there are the OSP(2N + 2 vertical bar 2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CPN-1 vertical bar N sigma models, while the former are conjecturally dual to supersphere sigma models. (C) 2011 Elsevier B.V. All rights reserved.