We analyse the conditions for AdS3​×M7​
backgrounds with pure NS-NS flux to be supersymmetric. We find that a necessary
condition is that M7​ is a U(1)-fibration over a
balanced manifold. We subsequently classify all N=(2,2) solutions
where M7​ satisfies the stronger condition of being a
U(1)-fibration over a Kahler 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.Comment: 39 pages; v2: minor corrections and references added; v3: section 2
shortened, final version as published in JHE