  We describe the general BPS system that governs the gravity duals of N=(0,2)
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 N=(0,2) system
to describe the gravity duals of SCFTs with N=(0,4) and N=(2,2) supersymmetry.
In the first case, the solutions fit in the larger class of AdS3xS2xCY3
solutions of M-theory dual to N=(0,4) SCFTs. In the case of the N=(2,2)
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.
