Yangian Superalgebras in Conformal Field Theory

TL;DR

This paper demonstrates the presence of Yangian symmetry in certain supergroup sigma models and conformal field theories, revealing new algebraic structures and their implications for correlation functions and dualities.

Contribution

It constructs non-local charges in supergroup conformal field theories and shows their Yangian symmetry, including its preservation under specific perturbations, expanding understanding of symmetries in these models.

Findings

Yangian symmetry is established in supergroup sigma models.

Correlation functions satisfy Ward identities due to Yangian symmetry.

Certain perturbations preserve the Yangian symmetry in these models.

Abstract

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 example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;\alpha) away from the WZW point. Further there are the OSP(2N+2|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 CP^{N-1|N} sigma models, while the former are conjecturally dual to supersphere sigma models.