Abstract
Abstract A brane-world SU(5) grand unified theory 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) → SU(3) × SU(2) × 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 ensures the vorticities of the SU(3) and SU(2) groups are identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of SU(3) (quarks) and 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) × SU(2) × 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.
Highlights
One of the most interesting paradigms of unified theories beyond the standard model is the brane-world scenario in which we live on a brane in higher-dimensional spacetime [1,2,3]
We show that other fields, except for a mixing part of the extra-dimensional component of the broken gauge fields and the scalar fields, are either massive or unphysical in the sense that they are absorbed by massive Kaluza–Klein (KK) towers of the gauge fields
In this work we have examined issues associated with the standard model (SM) gauge fields, gluons, weak bosons, and hypercharge U(1) gauge fields, their localization on the non-Abelian vortices as 3-branes in six-dimensional spacetime
Summary
One of the most interesting paradigms of unified theories beyond the standard model is the brane-world scenario in which we live on a brane in higher-dimensional spacetime [1,2,3]. If there is a vortex with k vorticity (k coincident vortices), the index theorem gives k zero modes for fermions This mechanism has previously been proposed to explain fermion generations in the brane-world scenario [48,49], the model was without the localization mechanism for gauge fields. Armed with our vector-analysis-like method, we show most importantly that the 3–2 splitting configuration of non-Abelian global vortices localizes the massless degrees of freedom corresponding to the SU(3) × SU(2) × U(1) SM gauge fields on the four-dimensional world-volume of the vortices. We leave it arbitrary for since it does not play any role in the rest of this section.2 It will play an important role, and we will clarify concrete conditions on B for a physically meaningful brane-world GUT model, namely the conditions for having massless gauge bosons localized on non-Abelian vortices.. This is not harmful for the construction of the effective theory of four-dimensional fields, as we explain in the subsequent sections
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