Wall and antiwall in the Randall-Sundrum model and a new infrared regularization

An approach to finding the field equation solution of the Randall-Sundrum model with the $S^1{/Z}_2$ extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the five-dimensional Higgs boson field. Both the domain wall and the anti-domain-wall naturally appear, at the ends of the extra compact axis, by taking a new infrared regularization. The solution is considered to be stable by the kink boundary condition. A continuous (infrared-) regularized solution, which is a truncated Fourier series of a discontinuous solution, is utilized. The ultraviolet-infrared relation appears in the regularized solution.