Abstract
We present a toy model that exhibits clash-of-symmetries style Higgs field kink configurations in a Randall-Sundrum-like spacetime. The model has two complex scalar fields Phi_{1,2}, with a sextic potential obeying global U(1)xU(1) and discrete Phi_1 <--> Phi_2 interchange symmetries. The scalar fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological constant. We show that the coupled Einstein-Higgs field equations have an interesting analytic solution provided the sextic potential adopts a particular form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sundrum type of spacetime. The thin-brane Randall-Sundrum limit, whereby the Higgs field kinks become step functions, is carefully defined in terms of the fundamental parameters in the action. The ``clash of symmetries'' feature, defined in previous papers, is manifested here through the fact that both of the U(1) symmetries are spontaneously broken at all non-asymptotic points in the extra dimension $w$. One of the U(1)'s is asymptotically restored as w --> -infinity, with the other U(1) restored as w --> +infinity. The spontaneously broken discrete symmetry ensures topological stability. In the gauged version of this model we find new flat-space solutions, but in the warped metric case we have been unable to find any solutions with nonzero gauge fields.
Highlights
The precise mechanism by which electroweak spontaneous symmetry breaking (SSB) happens has yet to be experimentally determined
The toy model we shall analyse consists of two complex scalar fields Φ1,2 coupled to 4 + 1 dimensional gravity endowed with a bulk cosmological constant
We have constructed a U(1)⊗U(1) model with two complex scalar fields interchanged by a discrete symmetry coupled to 4 + 1 dimensional gravity
Summary
The default SSB mechanism employed in the SM and many extensions to it utilises a simple spatially homogeneous, static and stable solution to the field equations: the Higgs fields φi(xμ) are set equal to those constant values corresponding to an absolute minimum of the Higgs potential. The energy densities required for electroweak and higher symmetry breaking are so high as to be incompatible with the strong evidence for a universe that is spatially homogeneous at large scales This objection, does not apply to brane-world models, because the non-trivial spatial dependence can be restricted to the extra dimension coordinates only. The boundary conditions at infinity for kink configurations are set to be the Higgs vacuum expectation values (VEVs) They force the spontaneous breaking G → H(|w| → ∞). The model-building promise of the clash of symmetries lies in the greater symmetry breaking power of spatially inhomogeneous Higgs configurations over the simple homogeneous alternative of standard SSB. We hope that this will lead to models with simpler Higgs sectors and fewer associated parameters. It is clear that the mechanisms are not identical, because the clash of symmetries has a physical Higgs field while the orbifold method is Higgsless
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