Double Yang-Baxter deformation of spinning strings

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We study the reduction of classical strings rotating in the deformed three- sphere truncation of the double Yang-Baxter deformation of theAdS(3)xS(3)xT(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.
© 2020 The Authors. We are grateful to J. M. Nieto for correspondence and a careful reading of the manuscript. This work is supported by grant PGC2018-095382-B-I00 and by BSCH-UCM through grant GR3/14-A 910770. R. R. acknowledges the support of the Universidad Complutense de Madrid through the predoctoral grant CT42/18-CT43/18. R. R. also acknowledges the organizers of the program YRISW 2020: a modern primer for superconformal field theories at DESY for support while this work was being completed.
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