A hidden symmetry of complex spacetime and the emergence of the standard model algebraic structure

TL;DR

This paper explores how extending spacetime into a complex manifold reveals a hidden symmetry that naturally leads to an algebraic structure similar to the standard model, bridging geometry and particle physics.

Contribution

It introduces a novel perspective on spacetime symmetry by considering complex manifolds and demonstrates how this leads to a standard model-like algebraic structure.

Findings

Mismatch between real and complex Poincaré group representations.

Implementation of spin^h structure induces standard model algebraic structure.

Complex spacetime extension reveals hidden symmetries.

Abstract

When spacetime is considered as a subspace of a wider complex spacetime manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. In particular, no spinors are allowed for the complex case. When a spin$^{h}$ structure is implemented on principal bundles in complex spacetime, one is naturally led to an algebraic structure analogous to the one of the standard model.