On Twistors and Conformal Field Theories from Six Dimensions

TL;DR

This paper explores six-dimensional twistorial structures and their applications to conformal field theories, providing new insights into twistor formulations and reductions to lower-dimensional theories, including a novel twistor space for self-dual strings.

Contribution

It offers a detailed cohomological analysis, develops Penrose and Penrose-Ward transforms, and introduces a new twistor space suitable for describing self-dual strings.

Findings

Developed twistor space action principles.

Derived contour integral formulae for field equations.

Discovered a novel twistor space for self-dual strings.

Abstract

We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, we explain the Penrose and Penrose-Ward transforms as well as contour integral formulae.