Integrable Deformations of Strings on Symmetric Spaces

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.

41 pages, typos corrected, references added

References in corpus (15)

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• Toda equations associated with loop groups of complex classical Lie groups

Cited by in corpus (4)

• Yang-Baxter sigma models based on the CYBE
• Spacetimes for λ-deformations
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions