Supersymmetry and the Nonlocal Yangian Deformation Symmetry

Abstract

In the quantized two-dimensional non-linear supersymmetric $σ$-model, the supercurrent supermultiplet, which contains the energy-momentum tensor, is transformed by the nonlocal symmetry of the model into the isospin current supermultiplet. This effect incorporates supersymmetry into the known infinite-dimensional Yangian deformation symmetry of plain $σ$-models, leads to precisely the same nontrivial extension of the two-dimensional super-Poincaré group as found previously for the Poincaré group, and thus determines the theory's mass spectrum. A generalization to all higher-order nonlocal charges is conjectured such that their generating function, the so-called ``master charge'', has a definite Lorentz spin which depends on the spectral parameter.