M2-branes on discs and multi-charged spindles

A bstract We study supersymmetric AdS 2 × Y 9 solutions of 11d supergravity where Y 9 is an S 7 fibration over a Riemann surface equipped with a metric of non-constant curvature. We consider two classes of Riemann surface: the first is a spindle and the second is a topological disc. These solutions are interpreted as the near-horizon limit of M2 branes wrapped on the Riemann surface and describe the near-horizon of a 4d black hole. In the case of the topological disc there are additional flavour M2 branes smeared on a five-sphere embedded in the transverse S 7 . We perform a full global analysis of both classes of solutions, both from a 4d and an 11d viewpoint. Finally we compute the two-dimensional Newton’s constant from which we obtain a prediction for the entropy of the black hole.