New $[SU(3)]^4$ Realization of Lepton/Dark Symmetry

TL;DR

This paper proposes a novel extension of the standard model with a fourfold gauge symmetry, incorporating a lepton/dark symmetry via a $Z_4$ symmetry, broadening the framework for understanding leptons and dark matter.

Contribution

It introduces a new realization of the $[SU(3)]^4$ gauge symmetry that includes a lepton/dark symmetry, extending previous models with an additional $SU(3)_N$ factor.

Findings

Develops a new gauge symmetry model with $[SU(3)]^4$

Incorporates a $Z_4$ symmetry to realize lepton/dark symmetry

Generalizes previous $SU(2)_N$ lepton symmetry models

Abstract

Extending the well-known $SU(3)_C \times SU(3)_L \times SU(3)_R$ model of quarks and leptons to include a fourth $SU(3)_N$ gauge factor, a new realization is obtained, different from leptonic color, which contains a lepton/dark symmetry with the help of an input $Z_4$ symmetry. It is seen to encompass a previous extension of the standard model to $SU(2)_N$ lepton symmetry.