Twistors and supertwistors for exceptional field theory

TL;DR

This paper explores twistor and supertwistor transforms in exceptional field theory, revealing how spinor parametrisation naturally solves key conditions and discussing implications for higher spin theories.

Contribution

It introduces twistor methods to analyze section conditions in exceptional field theory and extends them to supersymmetric cases with new invariance properties.

Findings

Spinor parametrisation solves mass-shell and section conditions.

Multi-particle twistors share a common section but are not orthogonal.

Supersymmetric extension includes kappa-symmetry invariants.

Abstract

As a means of examining the section condition and its possible solutions and relaxations, we perform twistor transforms related to versions of exceptional field theory with Minkowski signature. The spinor parametrisation of the momenta naturally solves simultaneously both the mass-shell condition and the (weak) section condition. It is shown that the incidence relations for multi-particle twistors force them to share a common section, but not to be orthogonal. The supersymmetric extension contains additional scalar fermionic variables shown to be kappa-symmetry invariants. We speculate on some implications, among them a possible relation to higher spin theory.