Left-Right Symmetric Model from Geometrical Formulation of Gauge Theory in $M_4 \times Z_2 \times Z_2$

TL;DR

This paper reconstructs the left-right symmetric model within a geometric framework using a product of Minkowski space and a discrete space, clarifying its structure and deriving more constrained Yukawa and Higgs terms.

Contribution

It presents a geometric formulation of the LRSM on a $M_4 imes Z_2 imes Z_2$ space, providing clearer structure and more restricted Yukawa and Higgs potential derivations.

Findings

Clarified geometric structure of LRSM

Derived restricted Yukawa coupling terms

Obtained constrained Higgs potential

Abstract

The left-right symmetric model (LRSM) with gauge group $SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L}$ is reconstructed from the geometric formulation of gauge theory in $M_4 \times Z_2 \times Z_2$ where $M_4$ is the four-dimensional Minkowski space and $Z_2 \times Z_2$ the discrete space with four points. The geometrical structure of this model becomes clearer compared with other works based on noncommutative geometry. As a result, the Yukawa coupling terms and the Higgs potential are derived in more restricted forms than in the standard LRSM.