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

TL;DR

This paper classifies supersymmetric AdS3 supergravity backgrounds with NS-NS flux, identifies their geometric structures, and confirms the holographic duality by matching BPS spectra with dual CFTs.

Contribution

It provides a complete classification of  solutions with specific geometric conditions and verifies the holographic correspondence through BPS spectrum matching.

Findings

Necessary condition:  fibration over a balanced manifold

Classification of  solutions with  fibration over Kahler manifolds

Matching of BPS spectra with dual CFTs

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.