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 (MSW) near-horizon with small superconformal symmetry and identify a class of AdS3 × S 2 × S 2 × 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.

We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and elevendimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS3 vacua pass routine stability tests.