The Effectiveness of Relativistic Invariance in AdS${}_3$

Abstract

We use relativistic invariance to investigate two aspects of integrable AdS${}_3$ string theory. Firstly, we write down the all-loop TBA equations for the massless sector of the theory with R-R flux, using the recently discovered hidden relativistic symmetry. Secondly, for the low-energy relativistic limit of the theory with NS-NS flux we write down the S matrix, dressing factors and TBA. We find that the integrable system coincides with a restriction to AdS${}_3$ of the relativistic q-deformed AdS${}_5$ theory. We also comment on the relativistic limit of the the small-$k$ NS-NS theory.

arXiv comment24 pages

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• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Massless S matrices for AdS3/CFT2
• Integrable Field Theories with an Interacting Massless Sector
• Integrable deformations of AdS/CFT
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Boost generator in AdS_3 integrable superstrings for general braiding
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
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• Norms and scalar products for AdS_3
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• A study of integrable form factors in massless relativistic $Ad{S}_2$
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes