Advances in Mathematical Physics
Volume 2009 (2009), Article ID 784215, 27 pages
Research Article

On the Mini-Superambitwistor Space and 𝒩=8 Super-Yang-Mills Theory

Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, R-30167 Hannover, Germany

Received 21 June 2008; Accepted 26 August 2008

Academic Editor: David B. Fairlie

Copyright © 2009 Christian Sämann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.