The low-energy limit of AdS3/CFT2 and its TBA
Diego Bombardelli (Department of Physics and INFN, University of Torino, Via P. Giuria 1, Torino, 10125, Italy); Bogdan Stefański (Centre for Mathematical Science, City, University of London, Northampton Square, London, EC1V 0HB, U.K.); Alessandro Torrielli (Department of Mathematics, University of Surrey, Guildford, GU2 7XH, U.K.)
We investigate low-energy string excitations in AdS3 × S3 × T4. 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 CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 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.