Quartification on an orbifold

We investigate quartification models in five dimensions, with the fifth dimension forming an $S^1/Z_2\times Z_2^{\prime }$ orbifold. The orbifold construction is combined with a boundary Higgs sector to break the quartified gauge group directly to a group $H\subset SU(3{)}^4$ which is operative at the electroweak scale. We consider $H=G_{\mathrm{SM}}\otimes SU(2{)}_{\ell }$ and $H=G_{\mathrm{SM}}$, where $G_{\mathrm{SM}}$ is the standard model gauge group, and find that unification occurs only when the remnant leptonic color symmetry $SU(2{)}_{\ell }$ remains unbroken. Furthermore, the demands of a realistic low-energy fermion spectrum specify a unique symmetry breaking route for the unifying case of $H=G_{\mathrm{SM}}\otimes SU(2{)}_{\ell }$. We contrast this with four-dimensional quartification models where unification may be achieved via a number of different symmetry breaking routes both with and without the remnant $SU(2{)}_{\ell }$ symmetry. The boundary Higgs sector of our model may be decoupled to achieve a Higgsless limit, and we show that the electroweak Higgs doublet may be identified as the fifth component of a higher-dimensional gauge field.