M2-branes on Discs and Multi-Charged Spindles

TL;DR

This paper constructs and analyzes supersymmetric AdS2 solutions in 11d supergravity with M2 branes wrapped on Riemann surfaces, providing insights into black hole near-horizon geometries and entropy calculations.

Contribution

It introduces new classes of AdS2 solutions with non-constant curvature Riemann surfaces, including spindles and discs, and performs a comprehensive global analysis.

Findings

Derived explicit supergravity solutions for M2 branes on spindles and discs.

Connected solutions to black hole near-horizon geometries and entropy.

Predicted black hole entropy from 2D Newton's constant.

Abstract

We study supersymmetric AdS$_2\times Y_9$ 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.