Large superconformal near-horizons from M-theory

We report on a classification of supersymmetric solutions to 11D supergravity with SO(2,2)×SO(3) isometry, which are AdS/CFT dual to 2D CFTs with N=(0,4) supersymmetry. We recover the Maldacena, Strominger, Witten near-horizon with small superconformal symmetry and identify a class of AdS3×S2×S2×CY2 geometries with emergent large superconformal symmetry. This exhausts known compact geometries. Compactification of M-theory on CY2 results in a vacuum of 7D supergravity with large superconformal symmetry, providing a candidate near-horizon for an extremal black hole and a potential new setting to address microstates.