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

摘要

We construct a new supertwistor space suited for establishing a Penrose-Wardtransform between certain bundles over this space and solutions to the𝒩=8super-Yang-Mills equations in three dimensions. This mini-superambitwistorspace is obtained by dimensional reduction of the superambitwistor space, thestandard superextension of the ambitwistor space. We discuss in detail the constructionof this space and its geometry before presenting the Penrose-Wardtransform. We also comment on a further such transform for purely bosonicYang-Mills-Higgs theory in three dimensions by considering third-order formal“subneighborhoods" of a miniambitwistor space.