Standard model on a domain-wall brane?

Abstract

We propose a $4+1$-dimensional action that is a candidate for realizing a standard-model-like effective theory for fields dynamically localized to a domain-wall brane. Our construction is in part based on the conjecture that the Dvali-Shifman mechanism for dynamically localizing gauge bosons to a domain wall works correctly in $4+1\mathrm{\text{\ensuremath{-}}}\mathrm{d}$. Assuming this to be so, we require the gauge symmetry to be SU(5) in the bulk, spontaneously breaking to $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ inside the domain wall, thus dynamically localizing the standard-model gauge bosons provided that the SU(5) theory in the bulk exhibits confinement. The wall is created jointly by a real singlet-Higgs field $\ensuremath{\eta}$ configured as a kink, and an SU(5) adjoint-Higgs field $\ensuremath{\chi}$ that takes nonzero values inside the wall. Chiral $3+1$-dimensional quarks and leptons are confined and split along the bulk direction via their Yukawa couplings to $\ensuremath{\eta}$ and $\ensuremath{\chi}$. The Higgs doublet and its color triplet SU(5) partner are similarly localized and split. The splittings can suppress colored-Higgs-induced proton decay and, because of the different localization profiles, the usual SU(5) mass relation ${m}_{e}={m}_{d}$ does not arise. Localized gravity is generated via the Randall-Sundrum alternative to compactification.