An Integrable Deformation of the AdS5 x S5 Superstring

TL;DR

This paper introduces a new integrable deformation of the AdS5 x S5 superstring sigma model, based on a quantum group symmetry at roots of unity, which preserves integrability and key symmetries.

Contribution

It presents a discrete deformation of the Green-Schwarz sigma model linked to a quantum group at roots of unity, expanding the understanding of deformed string backgrounds.

Findings

The deformed model remains integrable.

It retains the same equations-of-motion as the original model.

The deformation preserves a subset of kappa-symmetries.

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.