Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux

TL;DR

This work presents an exact, q-dependent generalization of the massive S-matrix for string theory on AdS_3 x S^3 x T^4 with mixed RR and NSNS flux. By preserving the same underlying symmetry algebra and modifying state representations via q, the authors derive an exact dispersion relation that interpolates between RR and NSNS limits and construct a factorized S-matrix that remains Yang-Baxter compliant. The q=0 case recovers the known exact S-matrix up to two phases, while the q≠0 case introduces x^±_{±} variables and four phases, with q=1 guiding a potential simplification akin to a WZW model. Together, these results lay the groundwork for a Bethe Ansatz, Y-system, and TBA analysis across the full q-range, enabling deeper exploration of the dual 2D CFT and integrable structure in mixed flux backgrounds.

Abstract

The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in arXiv:1303.5995.