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We describe the general BPS system that governs the gravity duals of \( \mathcal{N}=\left(0,\ 2\right) \) two-dimensional superconformal field theories in the low-energy limit of M5-branes on a four-manifold, M4. 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 M4. We further reduce the \( \mathcal{N}=\left(0,\ 2\right) \) system to describe the gravity duals of SCFTs with \( \mathcal{N}=\left(0,4\right) \) and \( \mathcal{N}=\left(2,2\right) \) supersymmetry. In the first case, the solutions fit in the larger class of AdS3 ×S2 × CY3 solutions of M-theory dual to \( \mathcal{N}=\left(0,4\right) \) SCFTs. In the case of the \( \mathcal{N}=\left(2,2\right) \) theories, the near-horizon limit of M4 is necessarily a product of two constant curvature Riemann surfaces whose metrics are governed by a pair of Liouville equations.

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