Puzzles of η-deformed AdS<inf>5</inf> Ã- S5

Abstract

We derive the part of the Lagrangian for the sigma model on the η -deformed AdS 5 × 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 La- grangian 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 equa- tions of motion, despite the presence of κ -symmetry. However, in a special scaling limit our solution reproduces the supergravity background found by Maldacena and Russo. Fur- ther, 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.