Twistor approach to higher-spin theories and matrix model

TL;DR

This paper explores how twistor theory can be used to formulate higher-spin theories and connect them to the IKKT matrix model, offering new methods for constructing local higher-spin actions and analyzing scattering amplitudes.

Contribution

It introduces a twistor-based framework for higher-spin theories, demonstrating how higher-spin symmetry can be encoded in twistor space and enabling the construction of local spacetime actions.

Findings

Higher-spin symmetry can be represented by hs-valued forms on twistor space

New local higher-spin actions can be derived from twistor space formulations

Some higher-spin theories exhibit non-trivial scattering amplitudes in flat space

Abstract

We discuss recent endeavours in connecting twistor theory to higher-spin theories and the IKKT- matrix model. Starting with a brief review on higher-spin algebra hs in four-dimensional target space, we elucidate how higher-spin symmetry can be encoded in hs-valued sections/holomorphic differential forms on (non-commutative) twistor space. This provides an efficient way to construct local higher-spin theories in spacetime from some actions on (non-commutative) twistor space. Remarkably, some higher-spin theories obtained within the framework of twistor theory can have non-trivial scattering amplitudes in flat space.