We study kink or domain wall solutions in $O\left(10\right)\mathrm{}$ Higgs models in the context of the “clash of symmetries” mechanism developed by Davidson, Toner, Volkas and Wali and, independently, by Pogosian and Vachaspati. We show that kink configurations employing Higgs fields in the $45$ (the adjoint representation) of $O\left(10\right)\mathrm{}$ break up into three classes: those that at finite distances from the wall respect a $U\left(5\right)\mathrm{}$ subgroup of $\mathrm{SO}\left(10\right),$ and two others that respect the smaller subgroups $U\left(3\right)\mathrm{}\otimes U\left(2\right)\mathrm{}$ and $U\left(4\right)\mathrm{}\otimes U\left(1\right).$ These smaller subgroups arise from the clash of symmetries mechanism: they are the intersections of two differently embedded $U\left(5\right)\mathrm{}$ subgroups of $\mathrm{SO}\left(10\right),$ the latter being the symmetries respected in asymptotia on opposite sides of the domain wall. The existence of the $\mathrm{SO}\left(10\right)\mathrm{}\to U\left(3\right)\mathrm{}\otimes U\left(2\right)=SU\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}\otimes U\left(1\right)\mathrm{}\otimes {U\left(1\right)\mathrm{}}^{\prime }\equiv G_{\mathrm{SM}}\otimes {U\left(1\right)\mathrm{}}^{\prime }$ class advances the search for a realistic brane world model wherein some of the required symmetry breaking is achieved via the clash of symmetries rather than the conventional mechanism. At the centers of the walls, the unbroken symmetries are enhanced. In the $U\left(3\right)\mathrm{}\otimes U\left(2\right)\mathrm{}$ case, the symmetry is $O\left(6\right)\mathrm{}\otimes U\left(2\right),$ which is closely related to the Pati-Salam-like $\mathrm{SU}\left(4\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}\otimes U\left(1\right)\mathrm{}$ group. If our universe is a brane located at the center of such a wall, then we see the $O\left(10\right)\mathrm{}$ symmetry as being strongly broken to $\mathrm{SU}\left(4\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}\otimes U\left(1\right).$ Interestingly, if the brane-world degrees of freedom enjoy a slight leakage off the wall, then an additional symmetry breakdown to $U\left(3\right)\mathrm{}\otimes {U\left(2\right)=G}_{\mathrm{SM}}\otimes {U\left(1\right)\mathrm{}}^{\prime }$ is effectively induced on the brane. This provides a possible framework within which to address at least part of a gauge hierarchy problem: $O\left(10\right)\mathrm{}$ is strongly broken to $\mathrm{SU}\left(4\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}\otimes U\left(1\right),$ then more weakly to $G_{\mathrm{SM}}\otimes {U\left(1\right)\mathrm{}}^{\prime }$ depending on the amount of leakage off the brane. We also comment on kinks employing the $10$ and $54$ of $O\left(10\right).$

• Received 21 August 2003

DOI:https://doi.org/10.1103/PhysRevD.69.045010