Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model

Abstract

We compute the tree-level bosonic S matrix in light-cone gauge for superstrings on pure-NSNS ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$. We show that it is proportional to the identity and that it takes the same form as for ${\text{AdS}}_3\times {\text{S}}^3\times {\text{T}}^4$ and for flat space. Based on this, we make a conjecture for the exact worldsheet S matrix and derive the mirror thermodynamic Bethe ansatz (TBA) equations describing the spectrum. Despite a non-trivial vacuum energy, they can be solved in closed form and coincide with a simple set of Bethe ansatz equations - again much like ${\text{AdS}}_3\times {\text{S}}^3\times {\text{T}}^4$ and flat space. This suggests that the model may have an integrable spin-chain interpretation. Finally, as a check of our proposal, we compute the spectrum from the worldsheet CFT in the case of highest-weight representations of the underlying Kač-Moody algebras, and show that the mirror-TBA prediction matches it on the nose.

38 pages, Version accepted for publication in JHEP

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• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• $T\bar{T}$ Flows and (2,2) Supersymmetry
• $T\bar{T}$ deformations and integrable spin chains
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• $T\bar{T}$ deformations as TsT transformations
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Massless S matrices for AdS3/CFT2
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• $T\overline{T}$ Deformations of nonrelativistic models
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Superstrings in Thermal Anti-de Sitter Space
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Geometry of Massless Scattering in Integrable Superstring
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• On exactly solvable Yang-Baxter models and enhanced symmetries
• Deforming integrable models of AdS${}_3$ strings
• Transfer matrices for AdS3/CFT2