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

TL;DR

This work classifies $\mathrm{AdS}_3$ backgrounds with pure NS-NS flux preserving $\text{N}=(2,2)$ supersymmetry by showing $\mathcal{M}_7$ must be a $\text{U}(1)$-fibration over a conformally balanced base, and, under the stronger Kahler condition, reduces to quotients of $\mathrm{S}^3\times\mathrm{CY}_2$ by finite groups. The authors completely classify the Kahler cases, identifying the Enriques surface and seven hyperelliptic surfaces as the only quotients yielding $\text{N}=(2,2)$, and compute their BPS spectra via a refined $\mathcal{N}=(4,4)$ multiplet analysis with twisted sectors. They propose dual CFTs as symmetric orbifolds $\mathrm{Sym}^\infty(\mathrm{ES})$ and $\mathrm{Sym}^\infty(\mathrm{HS})$ and verify spectral matches using the DMVV formula for chiral and anti-chiral sectors, establishing strong evidence for the proposed holographic duals. The results illuminate a controlled landscape of $\mathrm{AdS}_3$/CFT$_2$ pairs with $\mathcal{N}=(2,2)$ supersymmetry and pure NS-NS flux, and point to rich connections to higher-spin structures and moonshine in the Enriques/Hyperelliptic settings.

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.