$E_7$ as $D=10$ space-time symmetry --- Origin of the twistor transform

TL;DR

This paper develops an $E_7$-covariant framework for massless particle dynamics in 10-dimensional Minkowski space, linking space-time and twistor variables, and explores its relation to conformal symmetry and lower dimensions.

Contribution

It introduces an $E_7$-covariant formulation of massless particles in 10D, unifying space-time and twistor variables, and extends the approach to lower dimensions.

Findings

$E_7$ contains the conformal algebra as a subalgebra

The formulation applies to $D=10$, $D=3$, $D=4$, and $D=6$

Provides a new perspective on twistor transforms in higher dimensions

Abstract

Massless particle dynamics in $D=10$ Minkowski space is given an $E_7$-covariant formulation, including both space-time and twistor variables. $E_7$ contains the conformal algebra as a subalgebra. Analogous constructions apply to $D=3,4$ and 6.