The Six Dimensional Self-Dual Tensor

TL;DR

This paper derives and presents a six-dimensional Lorentz-covariant formulation of the equations of motion for a self-dual tensor, connecting it to M-theory five-brane dynamics and demonstrating equivalence with non-covariant formalisms.

Contribution

It provides a self-contained, covariant set of equations for a self-dual tensor in six dimensions, derived from M-theory five-brane equations, with a novel non-linear self-duality constraint.

Findings

Derived Lorentz-covariant equations of motion for self-dual tensor

Established equivalence with non-covariant formalism

Presented a non-linear self-duality constraint

Abstract

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant form. In particular, it is shown that the field-strength tensor satisfies a non-linear generalised self-duality constraint. The self-duality equation is rewritten in five-dimensional notation and shown to be identical to the corresponding equation in the non-covariant formalism.