Closed strings spinning in ${\mathrm{AdS}}_3\times S^3\times T^4$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three-form fluxes are described by a deformation of the one-dimensional Neumann–Rosochatius integrable system. In this article we find general solutions to this system that can be expressed in terms of elliptic functions. We consider closed strings rotating either in $S^3$ with two different angular momenta or in ${\mathrm{AdS}}_3$ with one spin. To find the solutions, we will need to extend the Uhlenbeck integrals of motion of the Neumann–Rosochatius system to include the contribution from the flux. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux, where the problem can be described by a supersymmetric Wess-Zumino-Witten model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.

• Received 30 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.126006