On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix

Abstract

We consider superstring theory on AdS_3 x S^3 x T^4 supported by a combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q). This theory interpolates between the pure RR flux model (q=0) whose spectrum is expected to be described by a Bethe ansatz and the pure NSNS flux model (q=1) which is described by the supersymmetric extension of the SL(2,R) x SU(2) WZW model. As a first step towards the solution of this integrable theory for generic value of q we compute the corresponding tree-level S-matrix for massive BMN-type excitations. We find that this S-matrix has a surprisingly simple dependence on q: the diagonal amplitudes have exactly the same structure as in the q=0 case but with the BMN dispersion relation e^2 = p^2 + 1 replaced by the one with shifted momentum and mass, e^2 = (p + q)^2 + 1 - q^2. The off-diagonal amplitudes are then determined from the classical Yang-Baxter equation. We also construct the Pohlmeyer reduced model corresponding to this superstring theory and find that it depends on q only through its mass-squared parameter proportional to (1-q^2), implying that its relativistic S-matrix is q-independent.

46 pages; v2: 50 pages, new part of Appendix A added and minor misprints corrected; v3: discussion of proposed dispersion relation in eq. 4.11 and symmetry algebra in appendix B for q not 0 modified; v4: minor corrections and comments added; v5: misprints corrected (in particular, in eqs. 3.18, 3.20 and 3.24) and reference added

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