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Type II supergravity admits an AdS(3) x S(2) x S(2) x T(3) solution withfluxes depending on several free parameters. We determine the constraints onthese parameters imposed by the requirement of (classical) integrability of thesuperstring sigma model. To do this we analyze the low-energy effective actionfor the spinning GKP string. The absence of particle production in thetree-level S-matrix of bosonic excitations is shown to imply the vanishing oftwo of the four parameters in the NSNS three-form flux. This reduces thesupergravity background to either the one-parameter AdS(3) x S(2) x S(2) x T(3)background preserving eight supersymmetries, or a non-supersymmetric branch,which differs only by flipping a sign in the RR flux. We show that both thesebranches can be obtained from AdS(3) x S(3) x S(3) x S(1) by T-dualities on the(Hopf) circle fibers of the three-spheres and therefore the integrability ofthe string in these backgrounds follows.

Integrability of the superstring in AdS(3) x S(2) x S(2) x T(3)