Supersymmetry and the Nonlocal Yangian Deformation Symmetry

TL;DR

This paper explores how supersymmetry integrates with the nonlocal Yangian deformation symmetry in two-dimensional supersymmetric sigma models, revealing implications for the theory's mass spectrum and proposing a generalization of nonlocal charges.

Contribution

It demonstrates the incorporation of supersymmetry into the Yangian deformation symmetry and extends the understanding of nonlocal charges in supersymmetric sigma models.

Findings

Supersymmetry is embedded into the Yangian symmetry of sigma models.

The mass spectrum is determined by the extended symmetry.

A conjecture on the Lorentz spin of the master charge is proposed.

Abstract

In the quantized two-dimensional non-linear supersymmetric $\sigma$-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 $\sigma$-models, leads to precisely the same nontrivial extension of the two-dimensional super-Poincar\'e group as found previously for the Poincar\'e 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.