3D supergravity from wrapped M5-branes

Abstract

Through consistent Kaluza-Klein reduction, we construct 3D $\mathcal{N} =2$ gauged supergravities corresponding to twisted compactifications of M5-branes on a product of constant curvature Riemann surfaces, including K\"{a}hler-Einstein four-manifolds. We extend the reduction to fermionic supersymmetry variations in order to determine the 3D Killing spinor equations and classify all timelike supersymmetric solutions. As a by-product, we identify an infinite class of new supersymmetric warped $AdS_3$ (G\"odel) and warped $d S_3$ solutions. Moreover, we show that the superpotential $T$ encodes the central charge and R symmetry of the dual $\mathcal{N} = (0,2)$ SCFTs in the large $N$ limit. We demonstrate that the R symmetry matches the canonical $U(1)$ isometry from existing classifications of supersymmetric $AdS_3$ solutions to 11D supergravity with $\mathcal{N} = (0,2)$ supersymmetry.