Clash of symmetries in a Randall-Sundrum-like spacetime

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 Φ1,2, with a sextic potential obeying global U(1)U(1) and discrete Φ1Φ2 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 nonasymptotic points in the extra dimension w. One of the U(1)'s is asymptotically restored as w→-, with the other U(1) restored as w→. 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.