Transition from SU(2)_L x SU(2)_R x U(1)_(B-L) Representation to SU(2)_L x U(1)_Y by q-Deformation and the Corresponding Classical Breaking Term of Chiral U(2)

TL;DR

This paper explores how q-deformation of SU(2) representations can model the transition from a left-right symmetric gauge group to the Standard Model's hypercharge group, linking algebraic deformation to symmetry breaking.

Contribution

It introduces a q-deformation approach to connect SU(2)_L x SU(2)_R x U(1)_{B-L} to the Standard Model's U(1)_Y, providing a novel algebraic perspective on symmetry breaking.

Findings

q-deformation maps LR symmetry to Standard Model hypercharge

Classical O(3)-breaking term modeled as magnetic field

Explicit parameter Delta controls symmetry transition

Abstract

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the vev and the hypercharge splitting (Delta) of right-handed leptons (quarks) in a family vanish and Q=T_0 + Y independently in each helicity sector. As a generalization, we start with SU(2)_L x SU(2)_R x U(1)_{(B-L)} and introduce Delta as a continuous parameter which is a measure of explicit symmetry breakdown. Values of Delta between zero and 1/2 take the neutral generator of the isospin-1/2 representation to the singlet representation, i.e. `deformes' the LR representation into the minimal Standard one. The corresponding classical O(3)-breaking term is a magnetic field perpendicular to the x_3-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.