Gauge-flavon unification

TL;DR

This paper introduces gauge-flavon unification, where flavons originate from extra-dimensional gauge fields, offering a new mechanism for flavon VEV alignment via Wilson lines and orbifold symmetry breaking.

Contribution

It proposes a novel gauge-flavon unification framework, providing explicit 5d models and a general formalism for Wilson lines and orbifolds applicable to multiple dimensions.

Findings

Presented simple 5d models with $SO(3)$ and $SU(4)$ symmetries.

Demonstrated flavon VEV alignment through Wilson lines.

Developed a formalism for orbifolds and Wilson lines in various dimensions.

Abstract

In this paper we propose the idea that flavons can emerge from extra dimensional gauge fields, referred to as gauge-flavon unification (GFU) analogous to gauge-Higgs unification (GHU). We assume that there is a gauged family symmetry in extra dimensions and that the flavons are the extra dimensional components of the gauge field. This provides a simple mechanism to align the VEVs of the flavons through a combination of Wilson lines and orbifold symmetry breaking. We present some simple 5d examples of GFU based on $SO(3)$ and $SU(4)$ gauged family symmetry, the latter case yielding $SU(3)\times U(1)$ gauged family symmetry in 4d, broken by triplet and antitriplet flavons, with effective couplings to fermions. We also present a general formalism for Wilson lines and orbifolds, in any number of dimensions, including non-commutative aspects Wilson lines, which may be useful for aligning additional flavons as required for realistic models.