Non-chiral current algebras for deformed supergroup WZW models

TL;DR

This paper investigates deformed supergroup WZW models with vanishing Killing form, deriving exact correlation functions and revealing non-local charges related to Yangian symmetry, with potential implications for string theory and condensed matter physics.

Contribution

It introduces a new class of deformed supergroup WZW models with exact correlation functions and uncovers non-local Yangian charges in these models.

Findings

Exact two- and three-point functions derived

Identification of non-local charges generating a Yangian

Analysis of operator product algebra and equations of motion

Abstract

We study deformed WZW models on supergroups with vanishing Killing form. The deformation is generated by the isotropic current-current perturbation which is exactly marginal under these assumptions. It breaks half of the global isometries of the original supergroup. The current corresponding to the remaining symmetry is conserved but its components are neither holomorphic nor anti-holomorphic. We obtain the exact two- and three-point functions of this current and a four-point function in the first two leading orders of a 1/k expansion but to all orders in the deformation parameter. We further study the operator product algebra of the currents, the equal time commutators and the quantum equations of motion. The form of the equations of motion suggests the existence of non-local charges which generate a Yangian. Possible applications to string theory on Anti-de Sitter spaces and to condensed matter problems are briefly discussed.