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

TL;DR

This paper introduces a new supertwistor space tailored for connecting geometric structures with solutions to N=8 super Yang-Mills equations in three dimensions, expanding the twistor approach to supersymmetric gauge theories.

Contribution

It constructs a novel mini-superambitwistor space via dimensional reduction and establishes a Penrose-Ward transform linking this space to super Yang-Mills solutions.

Findings

Constructed a new supertwistor space for N=8 super Yang-Mills in 3D.

Established a Penrose-Ward transform for this space.

Discussed a transform for bosonic Yang-Mills-Higgs 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 "sub-neighborhoods" of a mini-ambitwistor space.