Clash of symmetries on the brane

Abstract

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 $G_{\text{cts}}\otimes G_{\text{discrete}}$ symmetry is spontaneously broken to $H_{\text{cts}}\otimes H_{\text{discrete}}$, where the continuous subgroup $H_{\text{cts}}$ can be embedded in several different ways in the parent group $G_{\text{cts}}$, and $H_{\text{discrete}}<G_{\text{discrete}}$. A certain class of topological domain wall solutions connect two vacua that are invariant under {\it differently embedded} $H_{\text{cts}}$ 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 $H_{\text{cts}}$ 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 three-fold planar domain wall junction configuration, with our universe at the nexus. A possible connection with $E_6$ is discussed.

30 pages, 9 embedded figures

References in corpus (2)

• Space of kink solutions in SU(N)\times Z_2
• A class of kinks in SU(N)\times Z_2

Cited by in corpus (21)

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• Stability of domain walls coupled to Abelian gauge fields
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• On The Problem of Vacuum energy in Brane Theories
• Selfgravitating $SU(5)$ Higgs domain walls as a braneworlds
• Fermion Confinement in Brane World Models with SO(10) Unification
• Unified Dark Matter from a Simple Gauge Group on a Domain-Wall Brane