The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA

Abstract

We investigate low-energy string excitations in AdS${}_3\times$S${}^3\times$T${}^4$. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT${}_2$. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes' wrapping effects may be incorporated into the AdS${}_3$ spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low energy CFT${}_2$ to be $c=6$ from calculating the vacuum energy for antiperiodic fermions - with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory - and find the energies of some excited states.

47 pages, 5 figures. v2: typos fixed, comments and clarifications added, matches the published version

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Cited by in corpus (18)

• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Massless S matrices for AdS3/CFT2
• Integrable Field Theories with an Interacting Massless Sector
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Boost generator in AdS_3 integrable superstrings for general braiding
• A study of integrable form factors in massless relativistic AdS_3
• Geometry of Massless Scattering in Integrable Superstring
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Norms and scalar products for AdS_3
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes
• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix