SM gauge fields localized on non-Abelian vortices in 6 dimensions

TL;DR

This paper constructs a six-dimensional brane-world model with non-Abelian vortices that localize Standard Model gauge fields, achieving symmetry breaking, confinement, and generation of fermion zero modes, providing a geometric origin for the Standard Model structure.

Contribution

It introduces a novel 6D brane-world setup with non-Abelian vortices that realize gauge field localization, symmetry breaking, and fermion generation mechanisms in a unified geometric framework.

Findings

Localized massless $SU(3) imes SU(2) imes U(1)$ gauge fields on vortices.

Achieved $SU(5)$ to Standard Model symmetry breaking via geometric Higgs mechanism.

Established confinement and vortex stability through a deformation potential.

Abstract

A brane-world $SU(5)$ GUT model with global non-Abelian vortices is constructed in six-dimensional spacetime. We find a solution with a vortex associated to $SU(3)$ separated from another vortex associated to $SU(2)$. This $3-2$ split configuration achieves a geometric Higgs mechanism for $SU(5)\to SU(3)\times SU(2)\times U(1)$ symmetry breaking. A simple deformation potential induces a domain wall between non-Abelian vortices, leading to a linear confining potential. The confinement stabilizes the vortex separation moduli, and assures the vorticity of $SU(3)$ group and of $SU(2)$ group to be identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of $SU(3)$ (quarks) and of $SU(2)$ (leptons), leading to quark-lepton generations. The standard model massless gauge fields are localized on the non-Abelian vortices thanks to a field-dependent gauge kinetic function. We perform fluctuation analysis with an appropriate gauge fixing and obtain a four-dimensional effective Lagrangian of unbroken and broken gauge fields at quadratic order. We find that $SU(3) \times SU(2) \times U(1)$ gauge fields are localized on the vortices and exactly massless. Complications in analyzing the spectra of gauge fields with the nontrivial gauge kinetic function are neatly worked out by a vector-analysis like method.