Topological charges for branes in M-theory

TL;DR

This paper introduces a simplified superalgebra for M2 and M5-branes in 11D supergravity backgrounds, identifying topological charges and BPS bounds, generalizing calibration forms for supersymmetric backgrounds.

Contribution

It presents a new, unified superalgebra formulation that includes topological charges for branes in arbitrary supersymmetric backgrounds, extending previous results.

Findings

Identified topological charges as integrals of closed forms.

Derived BPS bounds for brane energies.

Generalized calibration forms for supersymmetric backgrounds.

Abstract

We propose a simple form for the superalgebra of M2 and M5-brane probes in arbitrary supersymmetric backgrounds of 11D supergravity, extending previous results in the literature. In particular, we identify the topological charges in the algebras and find BPS bounds for the energies. The charges are given by the integral over a brane's spatial worldvolume of a certain closed form built out of the Killing spinors and background fields. The existence of such closed forms for arbitrary supersymmetric backgrounds generalises the existence of calibration forms for special holonomy manifolds.