Aspects of the M5-Brane

TL;DR

This paper reviews the geometric constraints and equations of motion of the M5-brane, explores its embedding in different formalisms, and derives conditions on its partition function, advancing understanding of M-brane dynamics.

Contribution

It provides a comprehensive review of M5-brane equations of motion in superspace and component form, and introduces a simplified nonlinear self-duality condition for the worldvolume 2-form.

Findings

Derived a simplified second order field equation for the M5-brane's 2-form potential

Presented a nonlinear holomorphicity condition on the M5-brane partition function

Reviewed the embedding constraints from kappa symmetry and their implications

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.