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

## TL;DR

This paper leverages relativistic invariance to derive all-loop TBA equations for the massless sector of integrable AdS3 string theory with R-R flux and constructs the S matrix for the low-energy limit with NS-NS flux, revealing connections to q-deformed AdS5.

## Contribution

It introduces a novel use of relativistic symmetry to formulate TBA equations and S matrices in AdS3 string theory, linking it to q-deformed AdS5 models.

## Key findings

- Derived all-loop TBA equations for massless sector with R-R flux.
- Constructed S matrix and dressing factors for the low-energy NS-NS flux limit.
- Identified the integrable system as a restriction of q-deformed AdS5 theory.

## 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.