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

Abstract

Type II supergravity admits an AdS(3) x S(2) x S(2) x T(3) solution with fluxes depending on several free parameters. We determine the constraints on these parameters imposed by the requirement of (classical) integrability of the superstring sigma model. To do this we analyze the low-energy effective action for the spinning GKP string. The absence of particle production in the tree-level S-matrix of bosonic excitations is shown to imply the vanishing of two of the four parameters in the NSNS three-form flux. This reduces the supergravity 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 these branches 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 of the string in these backgrounds follows.

11 pages, 1 figure; v3: Minor clarifications, matches published version

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• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Chaos Bound and its violation in Black p-brane
• Analytic Non-Integrability and S-Matrix Factorization
• Non-integrability of the $\Omega$-deformation
• Tree level integrability in 2d quantum field theories and affine Toda models
• Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA