Large superconformal near-horizons from M-theory

We report on a classification of supersymmetric solutions to 11D supergravity with $SO(2,2) \times SO(3)$ isometry, which are AdS/CFT dual to 2D CFTs with $\mathcal{N} = (0,4)$ supersymmetry. We recover the Maldacena, Strominger, Witten (MSW) near-horizon with small superconformal symmetry and identify a class of $AdS_3 \times S^2 \times S^2 \times CY_2$ geometries with emergent large superconformal symmetry. This exhausts known compact geometries. Compactification of M-theory on $CY_2$ 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.