Clash of symmetries on the brane

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 G_cts ⊗ G _discrete symmetry is spontaneously broken to H_cts ⊗ H _discrete, where the continuous subgroup H_cts can be embedded in several different ways in the parent group G_cts , and H _discrete < G_discrele. A certain class of topological domain wall solutions connects two vacua that are invariant under differently embedded H_cts 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 H_cts 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.