If our (3 + 1)-dimensional universe is a brane or domain wall embedded in a higher dimensional space, then a phenomenon we term the "clash of symmetries" provides a new method of breaking some continuous symmetries. A global Gcts ⊗ G discrete symmetry is spontaneously broken to Hcts ⊗ H discrete, where the continuous subgroup Hcts can be embedded in several different ways in the parent group Gcts , and H discrete < Gdiscrele. A certain class of topological domain wall solutions connects two vacua that are invariant under differently embedded Hcts subgroups. There is then enhanced symmetry breakdown to the intersection of these two subgroups on the domain wall. This is the "clash." In the brane limit, we obtain a configuration with Hcts symmetries in the bulk but the smaller intersection symmetry on the brane itself. We illustrate this idea using a permutation symmetric three-Higgs-triplet toy model exploiting the distinct I-, U- and V- spin U(2) subgroups of U(3). The three disconnected portions of the vacuum manifold can be treated symmetrically through the construction of a threefold planar domain wall junction configuration, with our universe at the nexus. A possible connection with E6 is discussed.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)