A Clash-of-Symmetries Mechanism from Intersecting Domain-Wall Branes

We present a new Clash-of-Symmetries mechanism in the context of an intersecting domain-wall brane model in 5+1-dimensional Minkowskian spacetime recently proposed by the authors. This new application of the Dvali-Shifman idea is designed for localizing gauge fields on a domain-wall intersection and we employ it by adding a gauge group $G$ and giving the scalar fields which form lump-like profiles gauge charges. These fields in turn break $G$ to two different subgroups $H_{1}$ and $H_{2}$ on each domain wall, and the gauge fields of these subgroups are taken to be localized to the respective walls by the confinement dynamics of $G$. There is then a further breaking on the domain-wall intersection to $H_{1}\cap{}H_{2}$ and gauge fields of this overlap group can then be localized to the intersection if they belong inside non-Abelian subgroups of both $H_{1}$ and $H_{2}$ which are spontaneously broken on the intersection and confining in the 4+1D bulks of the respective domain-wall branes. This mechanism has some similarities to the Clash-of-Symmetries mechanism on a single domain wall except that in this case $H_{1}$ and $H_{2}$ need not be isomorphic. We then give some interesting examples of the mechanism in an SU(7) gauge theory, several of which result in the localization of the Standard Model gauge group.