On the mini-superambitwistor space and N = 8 super-Yang-Mills theory

Abstract

We construct a new supertwistor space suited for establishing a Penrose-Ward transform between certain bundles over this space and solutions to the N = 8 super-Yang-Mills equations in three dimensions. This mini-superambitwistor space is obtained by dimensional reduction of the superambitwistor space, the standard superextension of the ambitwistor space. We discuss in detail the construction of this space and its geometry before presenting the Penrose-Ward transform. We also comment on a further such transform for purely bosonic Yang-Mills-Higgs theory in three dimensions by considering third-order formal "subneighborhoods" of a miniambitwistor space. Copyright © 2009 Christian Sämann.