Supersymmetric Gauge Theories in Twistor Space

TL;DR

The paper presents a twistorial action for N=4 SYM on PT^{3|4} comprising a holomorphic Chern-Simons term and a log-determinant term, and proves its perturbative equivalence to spacetime N=4 SYM while avoiding conformal supergravity. It shows how fibre integration from twistor space yields the full spacetime action and how an axial gauge naturally leads to the MHV diagram structure, with extensions to N=2, N=1, and matter multiplets via symmetry reductions. The work contrasts this construction with Witten’s original twistor-string, arguing for a clean, single-trace, gravity-free description and proposing close connections to a modified twistor-string framework. Together, these results provide a concrete, gauge-invariant, twistor-space formulation of N=4 SYM and a clear path toward lower-supersymmetry theories and loop-level explorations.

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.