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 $\mathrm{AdS}/\mathrm{CFT}$ dual to 2D CFTs with $\mathcal{N}=(0,4)$ supersymmetry. We recover the Maldacena, Strominger, Witten near-horizon with small superconformal symmetry and identify a class of ${\mathrm{AdS}}_3\times S^2\times S^2\times C{Y}_2$ geometries with emergent large superconformal symmetry. This exhausts known compact geometries. Compactification of M-theory on $C{Y}_2$ 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.