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

TL;DR

This paper derives the exact worldsheet S-matrix for type IIB strings on AdS3×S3×S3×S1 with mixed fluxes, including massive and massless modes, by analyzing the symmetry algebra and crossing equations.

Contribution

It provides the first non-perturbative S-matrix for this background, incorporating both massive and massless excitations with phase factors satisfying crossing symmetry.

Findings

Derived the off-shell symmetry algebra and its representations.

Determined the non-perturbative worldsheet S-matrix including phase factors.

Analyzed crossing equations and commented on heavy mode nature.

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.