Spacetime is Right-handed

TL;DR

This paper explores a novel right-handed spinor framework in complex spacetime, leading to chiral formulations of fundamental theories and a distinctive Euclidean spacetime symmetry structure.

Contribution

It introduces an unconventional chirally asymmetric approach using right-handed spinors, redefining spacetime and internal symmetries in Euclidean and Minkowski contexts.

Findings

Self-dual two-forms enable chiral formulations of Yang-Mills and gravity.

Euclidean spacetime left-handed spinors transform under an internal SU(2) symmetry.

The approach offers a new perspective on spacetime and internal symmetry relations.

Abstract

We describe the relation between vectors and spinors in complex spacetime in an unconventional chirally asymmetric manner, using purely right-handed spinors, with Minkowski spacetime getting Wick rotated to a four-dimensional Euclidean spacetime with a distinguished direction. In this right-handed spinor geometry self-dual two-forms can be used to get chiral formulations of the Yang-Mills and general relativity actions. Euclidean spacetime left-handed spinors then transform under an internal $SU(2)$ symmetry, rather than the usual $SU(2)_L$ spacetime symmetry related by analytic continuation to the Lorentz group $SL(2,\mathbf C)$.