# String theory on $\boldsymbol{\text{AdS}_{\mathbf{3}}}$ and the symmetric orbifold of Liouville theory

## TL;DR

This paper constructs DDF operators for string theory on AdS3 with NS-NS flux, revealing the spacetime symmetry algebra and identifying the dual CFT as a symmetric orbifold of Liouville theory combined with T^4, with special cases matching known results.

## Contribution

It explicitly constructs DDF operators and identifies the dual CFT as a symmetric orbifold of Liouville theory times T^4, extending previous understanding of AdS3/CFT2 correspondence.

## Key findings

- Dual CFT is symmetric orbifold of Liouville theory and T^4 for generic flux.
- Liouville factor disappears at minimal flux, reducing to symmetric orbifold of T^4.
- Analysis applies to both superstring and bosonic string theories on AdS3.

## Abstract

For string theory on AdS$_3$ with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows us to show that the CFT dual of superstring theory on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ for generic NS-NS flux is the symmetric orbifold of $({\cal N}=4$ Liouville theory$)\times \mathbb{T}^4$. For the case of minimal flux ($k=1$), the Liouville factor disappears, and we just obtain the symmetric orbifold of $\mathbb{T}^4$, thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on ${\rm AdS}_3 \times X$.