Unification mechanism for gauge and spacetime symmetries

TL;DR

This paper introduces a novel group-theoretical mechanism that unifies gauge and spacetime symmetries by relaxing traditional constraints, enabling a supersymmetry-like extension without exotic particles, and overcoming established no-go theorems.

Contribution

It proposes a minimal condition on gauge groups for unification, allowing a non-conventional extension that bypasses no-go theorems without requiring new particles.

Findings

Mathematically demonstrated the possibility of the unification mechanism.

Shown that the relaxed gauge group condition aligns with energy positivity.

Illustrated the mechanism within a U(1) gauge theory setting.

Abstract

A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so called Levi factor of the gauge group needs to be compact semisimple, not the entire gauge group. This allows a non-conventional supersymmetry-like extension of the gauge group, glueing together the gauge and spacetime symmetries, but not needing any new exotic gauge particles. It is shown that this new relaxed requirement on the gauge group is nothing but the minimal condition for energy positivity. The mechanism is demonstrated to be mathematically possible and physically plausible on a U(1) based gauge theory setting. The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman-Mandula no-go theorems in a non-supersymmetric way.