An integrable deformation of the AdS5 × S5 superstring

The S-matrix on the world-sheet theory of the string in AdS 5 × S 5 ?> 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 kth 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.