Quartification on an orbifold

Abstract

We investigate quartification models in five dimensions, with the fifth dimension forming an ${S}^{1}/{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}^{\ensuremath{'}}$ orbifold. The orbifold construction is combined with a boundary Higgs sector to break the quartified gauge group directly to a group $H\ensuremath{\subset}SU(3{)}^{4}$ which is operative at the electroweak scale. We consider $H={G}_{\mathrm{SM}}\ensuremath{\bigotimes}SU(2{)}_{\ensuremath{\ell}}$ 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 $SU(2{)}_{\ensuremath{\ell}}$ remains unbroken. Furthermore, the demands of a realistic low-energy fermion spectrum specify a unique symmetry breaking route for the unifying case of $H={G}_{\mathrm{SM}}\ensuremath{\bigotimes}SU(2{)}_{\ensuremath{\ell}}$. 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 $SU(2{)}_{\ensuremath{\ell}}$ 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.