An Integrable Deformation of the AdS5 x S5 Superstring

Abstract

The S-matrix on the world-sheet theory of the string in AdS5 x S5 has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a particular deformation of the Green-Schwarz sigma model. An interpretation of the case with q a root of unity has, until now, been lacking. We show that the Green-Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the F/F_V gauged WZW model, where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity where k is the level. The deformed theory has the same equations-of-motion as the Green-Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.

23 pages, improved and expanded discussion of metric and B field

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• Doubled aspects of generalised dualities and integrable deformations
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• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrable Deformations of Sigma Models
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• $T$-folds from Yang-Baxter deformations
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
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• $\lambda$-deformations of left-right asymmetric CFTs
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