Aspects of the M5-Brane

TL;DR

This work analyzes the M5-brane within M-theory by examining the κ-symmetry of an open M2 ending on the M5, deriving covariant embedding constraints that produce the M5-brane equations of motion in both superspace and Green-Schwarz form. It introduces a non-chiral formulation with an unconstrained 2-form potential and a nonlinear self-duality condition, relating it to a scale-invariant action and demonstrating the equivalence to the chiral M5 theory through holomorphic constraints on the partition function. The paper also develops a covariant set of M5-brane equations of motion, clarifies the role of a worldvolume self-dual 3-form, and provides explicit nonlinear self-duality relations that govern the dynamics. Overall, it connects the geometric superembedding approach to action-based formulations, including dualities, and clarifies how chiral and non-chiral descriptions are reconciled for the M5-brane.

Abstract

The kappa symmetry of an open M2-brane ending on an M5-brane requires geometrical constraints on the embedding of the system in target superspace. These constraints lead to the M5-brane equations of motion, which we review both in superspace and in component (i.e. in Green-Schwarz) formalism. We also describe the embedding of the chiral M5-brane theory in a non-chiral theory where the equations of motion follow from an action that involves a non-chiral 2-form potential, upon the imposition of a non-linear self-duality condition. In this formulation, we find a simplified form of the second order field equation for the worldvolume 2-form potential, and we derive the nonlinear holomorphicity condition on the partition function of the chiral M5-brane.