Puzzles of eta-deformed AdS_5 x S^5

TL;DR

This paper derives the fermionic part of the eta-deformed AdS_5 x S^5 superstring Lagrangian, explores its relation to supergravity backgrounds, and analyzes the integrability and scattering matrix properties of the model.

Contribution

It provides a fermionic Lagrangian for eta-deformed AdS_5 x S^5, shows the associated RR couplings do not satisfy supergravity equations, and demonstrates the integrability of the scattering matrix.

Findings

Fermionic Lagrangian can be brought to standard form via field redefinition.

RR couplings do not satisfy supergravity equations of motion.

The scattering matrix factorizes and satisfies the classical Yang-Baxter equation.

Abstract

We derive the part of the Lagrangian for the sigma model on the eta-deformed AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the corresponding Lagrangian to the standard form of type IIB Green-Schwarz superstring. Reading off the corresponding RR couplings, we observe that they fail to satisfy the supergravity equations of motion, despite the presence of kappa-symmetry. However, in a special scaling limit our solution reproduces the supergravity background found by Maldacena and Russo. Further, using the fermionic Lagrangian, we compute a number of new matrix elements of the tree level world-sheet scattering matrix. We then show that after a unitary transformation on the basis of two-particle states which is not one-particle factorisable, the corresponding T-matrix factorises into two equivalent parts. Each part satisfies the classical Yang-Baxter equation and coincides with the large tension limit of the q-deformed S-matrix.