Supersymmetric AdS${}_3$ supergravity backgrounds and holography

We analyse the conditions for ${AdS}_3\times M_7$ backgrounds with pure NS-NS flux to be supersymmetric. We classify all $N=(2,2)$ solutions where $M_7$ satisfies the stronger condition of being a $U\left(1\right)$-fibration over a Kähler manifold. We compute the BPS spectrum of all the backgrounds in this classification. We assign a natural dual CFT to the backgrounds and confirm that the BPS spectra agree, thus providing evidence in favour of the proposal.