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

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.

42 pages, Mathematica file included

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Cited by in corpus (5)

• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Norms and scalar products for AdS_3
• Finite size effect from classical strings in $Ad{S}_3\times S^3$ with NS-NS flux
• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix