Gravity duals of $$ \mathcal{N}=\left(0,\ 2\right) $$ SCFTs from M5-branes

Abstract

Abstract We describe the general BPS system that governs the gravity duals of $$ \mathcal{N}=\left(0,\ 2\right) $$ N = 0 , 2 two-dimensional superconformal field theories in the low-energy limit of M5-branes on a four-manifold, M 4. In order to preserve supersymmetry, we restrict to cases where the four-manifold is embedded in a Calabi-Yau fourfold that is a sum of two line bundles over M 4. We further reduce the $$ \mathcal{N}=\left(0,\ 2\right) $$ N = 0 , 2 system to describe the gravity duals of SCFTs with $$ \mathcal{N}=\left(0,4\right) $$ N = 0 4 and $$ \mathcal{N}=\left(2,2\right) $$ N = 2 2 supersymmetry. In the first case, the solutions fit in the larger class of AdS 3 ×S 2 × CY 3 solutions of M-theory dual to $$ \mathcal{N}=\left(0,4\right) $$ N = 0 4 SCFTs. In the case of the $$ \mathcal{N}=\left(2,2\right) $$ N = 2 2 theories, the near-horizon limit of M 4 is necessarily a product of two constant curvature Riemann surfaces whose metrics are governed by a pair of Liouville equations.