  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.
