A Gauge Field Model On $SU(2)_L\times SU(2)_R\times U(1)_Y \times \pi_4(G_{YM})$

TL;DR

This paper reconstructs a left-right symmetric gauge model incorporating a discrete gauge group derived from $A4$-homotopy, integrating Higgs fields as gauge fields within a non-commutative geometric framework.

Contribution

It introduces a novel gauge-theoretic formulation of a left-right symmetric model with Higgs fields as gauge fields on a discrete group, extending non-commutative geometry methods.

Findings

Higgs fields are modeled as gauge fields on a discrete gauge group.

The gauge group includes a $A4$-homotopy component, enriching the symmetry structure.

The model aligns with principles of non-commutative geometry.

Abstract

We reconstruct the Lagrangian of a left-right symmetric model with the gauge group $SU(2)_L\times SU(2)_R\times U(1)_Y \times \pi_4(SU(2)_L\times SU(2)_R\times U(1)_Y) $. The Higgs fields appear as gauge fields on discrete gauge group $\pi_4(SU(2)_L\times SU(2)_R\times U(1)_Y) $ and are assigned in a way complying with the principle that both the original gauge group $G_{YM}$ and the discrete group $\pi_4(G_{YM})$ should be taken as gauge groups in sense of non-commutative geometry.