Double Yang-Baxter deformation of spinning strings

Abstract

We study the reduction of classical strings rotating in the deformed threesphere truncation of the double Yang-Baxter deformation of the AdS 3 ×S 3 ×T 4 background to an integrable mechanical model. The use of the generalized spinning-string ansatz leads to an integrable deformation of the Neumann-Rosochatius system. Integrability of this system follows from the fact that the usual constraints for the Uhlenbeck constants apply to any deformation that respects the isometric coordinates of the three-sphere. We construct solutions to the system in terms of the underlying ellipsoidal coordinate. The solutions depend on the domain of the deformation parameters and the reality conditions of the roots of a fourth order polynomial. We obtain constant-radii, giant-magnon and trigonometric solutions when the roots degenerate, and analyze the possible solutions in the undeformed limit. In the case where the deformation parameters are purely imaginary and the polynomial involves two complex-conjugated roots, we find a new class of solutions. The new class is connected with twofold giant-magnon solutions in the degenerate limit of infinite period.

Boost generator in AdS3 integrable superstrings for general braiding

“…In this section we will study a coproduct characterised by the following braiding of the supercharges the algebra consistent with the coproduct of the momentum. The first coproduct and the R-matrix associated to it correspond to the massless limit of the ones studied in [72] (see also [80][81][82][83][84][85][86]) while the second one has not appeared in the literature yet to our knowledge.…”

Neumann-Rosochatius system for rotating strings in AdS3 × S3 × S3 × S1 with flux

“…. Being one of the earliest classical integrable model, NR model has been studied as an exemplary ground to compute for large class of string solutions in various integrable 10d AdS d ×X 10−d backgrounds with or without flux by means of some generic NR ansatz [45][46][47][48][49][50][51][52][53][54][55][56][57]. The appearance of NR model is approved to be quite robust for many deformed backgrounds as well as for some probe strings other than fundamental ones.…”