The Effectiveness of Relativistic Invariance in AdS${}_3$

Abstract

We use relativistic invariance to investigate two aspects of integrable AdS${}_3$ string theory. Firstly, we write down the all-loop TBA equations for the massless sector of the theory with R-R flux, using the recently discovered hidden relativistic symmetry. Secondly, for the low-energy relativistic limit of the theory with NS-NS flux we write down the S matrix, dressing factors and TBA. We find that the integrable system coincides with a restriction to AdS${}_3$ of the relativistic q-deformed AdS${}_5$ theory. We also comment on the relativistic limit of the the small-$k$ NS-NS theory.