Routing (electronic design automation)

Theoretical physics

Supersymmetry

Riemann surface

Curvature

Pure mathematics

Mathematical physics

Homotopy

Computer science

Constant curvature

Computer network

Brane cosmology

Routing protocol

Physics

Mathematics

Link-state routing protocol

Geometry

Supergravity

Combinatorics

Fibration

Black hole (networking)

Topology (electrical circuits)

Topological entropy

Journal of High Energy Physics

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.

M2-branes on discs and multi-charged spindles