If our $\mathrm{}(3+1)\mathrm{}$-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 $G_{\mathrm{cts}}\otimes G_{\mathrm{discrete}}$ symmetry is spontaneously broken to $H_{\mathrm{cts}}\otimes H_{\mathrm{discrete}},$ where the continuous subgroup $H_{\mathrm{cts}}$ can be embedded in several different ways in the parent group $G_{\mathrm{cts}},$ and $H_{\mathrm{discrete}}<G_{\mathrm{discrete}}.$ A certain class of topological domain wall solutions connects two vacua that are invariant under differently embedded $H_{\mathrm{cts}}$ 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 $H_{\mathrm{cts}}$ 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 $V-\mathrm{spin}$ 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 $E_6$ is discussed.

• Received 7 February 2002

DOI:https://doi.org/10.1103/PhysRevD.65.125013