Supersymmetric ${\mathrm{AdS}}_3$ supergravity backgrounds and holography

Abstract

We analyse the conditions for ${\mathrm{AdS}}_3\times {\mathcal{M}}_7$ backgrounds with pure NS-NS flux to be supersymmetric. We find that a necessary condition is that ${\mathcal{M}}_7$ is a $\mathrm{U}(1)$-fibration over a balanced manifold. We subsequently classify all $\mathcal{N}=(2,2)$ solutions where ${\mathcal{M}}_7$ satisfies the stronger condition of being a $\mathrm{U}(1)$-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.

39 pages; v2: minor corrections and references added; v3: section 2 shortened, final version as published in JHEP

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