The six-dimensional self-dual tensor

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-sttrength 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.