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Puzzles of \(\eta\) deformed \(\mathrm{AdS}_{5}\times S^{5}\). (English) Zbl 1388.83726
Summary: We derive the part of the Lagrangian for the sigma model on the \(\eta\)-deformed \(\mathrm{AdS}_5\times \mathrm S^5\) 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 J. M. Maldacena and J. G. Russo [ibid. 1999, No. 9, Paper No. 25, 19 p. (1999; Zbl 0957.81083)]. 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.

MSC:
83E50 Supergravity
81V35 Nuclear physics
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