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arXiv · 2105.06026

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

Masato Arai·Filip Blaschke·Minoru Eto·Masaki Kawaguchi·Norisuke Sakai
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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.

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Masato Arai, Filip Blaschke, Minoru Eto, Masaki Kawaguchi, Norisuke Sakai. 2021-08-26. SM gauge fields localized on non-Abelian vortices in 6 dimensions. https://arxiv.org/abs/2105.06026

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