An approach to find 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 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the { \it ends} of the extra compact axis, by taking a { \it new infrared regularization}. The stability is guaranteed from the outset by the kink boundary condition. A { \it continuous} (infrared-)regularized solution, which is a truncated { \it Fourier series} of a { \it discontinuous} solution, is utilized.The ultraviolet-infrared relation appears in the regularized solution.
Categories: hep-th hep-ph