Supersymmetric Gauge Theories in Twistor Space

TL;DR

This paper develops a twistor space action for N=4 super Yang-Mills theory, establishing its equivalence to the spacetime formulation, and extends the approach to theories with less supersymmetry and matter coupling.

Contribution

It introduces a new twistor space action for supersymmetric gauge theories, avoiding conformal supergravity issues and enabling matter coupling.

Findings

The twistor space action matches the spacetime theory at perturbative level.

The approach is extended to theories with N<4 supersymmetry.

Matter multiplets can be coupled within the twistor framework.

Abstract

We construct a twistor space action for N=4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor actions for gauge theories with N<4 supersymmetry, and show how matter multiplets may be coupled to the gauge sector.