Integrable Deformations of Strings on Symmetric Spaces

TL;DR

This paper introduces a new class of integrable deformations for sigma-models on symmetric spaces, preserving integrability and equations of motion, and connects these deformations to known theories like the symmetric space sine-Gordon model.

Contribution

It presents a novel deformation method involving non-abelian T duality and gauged WZW models, extending integrability to a broader class of string theories on symmetric spaces.

Findings

Deformations preserve integrability and equations of motion.

Deformed symplectic structure involves a combination of original and Faddeev-Reshetikhin brackets.

Large coupling limit yields the symmetric space sine-Gordon theory.

Abstract

A general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on R x F/G via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5 x S5.