Covariant Field Equations of the M Theory Five-Brane

TL;DR

This work derives covariant six-dimensional equations of motion for the eleven-dimensional M-theory five-brane from superspace via the superembedding approach, making κ-symmetry emerge from worldvolume diffeomorphisms and avoiding the need for an auxiliary scalar. The component Green-Schwarz form is obtained, clarifying the roles of the self-dual 3-form and the embedding geometry. A double dimensional reduction to a ten-dimensional 4-brane reproduces the Born-Infeld dynamics, linking the M5-brane to the familiar D-brane framework and generalizing Born-Infeld structure to include a worldvolume chiral 2-form. The results offer a covariant, non-perturbative handle on M-brane dynamics with potential implications for solitons, quantization, and broader p-brane unification within M-theory.

Abstract

The component form of the equations of motion for the 5-brane in eleven-dimensions is derived from the superspace equations. These equations are fully covariant in six-dimensions. It is shown that double-dimensional reduction of the bosonic equations gives the equations of motion for a 4-brane in ten dimensions governed by the Born-Infeld action.