The low-energy limit of AdS3/CFT2 and its TBA

Abstract

A bstract We investigate low-energy string excitations in AdS 3 × S 3 × 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.