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

TL;DR

This work derives the tree-level S-matrix for massive BMN-type excitations of strings on $AdS_3 \times S^3 \times T^4$ with mixed RR/NSNS flux, parametrized by $q$. The diagonal S-matrix elements retain the same form as the pure-RR case but with the dispersion relation deformed to $e^2 = (p\pm q)^2 + 1 - q^2$, while off-diagonal entries are fixed by the classical Yang-Baxter equation, preserving integrability. The analysis extends from the bosonic $S^3$ sector to the full superstring, revealing a factorized, symmetry-consistent S-matrix that can be written as two copies of a deformed $[\mathfrak{psu}(1|1)^2]$-based S-matrix; the Pohlmeyer-reduced model exhibits a mass rescaling $\mu \to \sqrt{1-q^2}\,\mu$, making the relativistic S-matrix $q$-independent. These results set the stage for an all-orders Bethe ansatz and provide a bridge between the pure RR and pure NSNS regimes, with implications for AdS/CFT in the interpolating theory.

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.