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

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