The $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ worldsheet S matrix

TL;DR

The authors construct an all-loop worldsheet S matrix for type IIB strings on AdS3 x S3 x S3 x S1 with mixed RR/NSNS flux by deriving the off-shell symmetry algebra A from a gauge-fixed Green-Schwarz action. They classify massive and massless representations, develop exact representations via Zhukovski variables, and show that the S matrix is fixed by A up to a finite set of dressing factors, which are constrained by unitarity and crossing. The scattering data is organized into blocks by mass and chirality, with a comprehensive set of crossing equations and LR symmetry relations governing the dressing factors; the heavy modes are discussed as potential composites or bound states. This work establishes a three-parameter integrable family controlled by the string tension, flux parameter q, and geometry α, enabling potential advances toward Bethe Ansatz, finite-gap equations, and a deeper holographic understanding of AdS3/CFT2 with mixed flux.

Abstract

We investigate type IIB strings on $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ with mixed Ramond-Ramond (R-R) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) flux. By suitably gauge-fixing the closed string Green-Schwarz (GS) action of this theory, we derive the off-shell symmetry algebra and its representations. We use these to determine the non-perturbative worldsheet S-matrix of fundamental excitations in the theory. The analysis involves both massive and massless modes in complete generality. The S-matrix we find involves a number of phase factors, which in turn satisfy crossing equations that we also determine. We comment on the nature of the heaviest modes of the theory, but leave their identification either as composites or bound-states to a future investigation.