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

Understand

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.