Wall and Anti-Wall in the Randall-Sundrum Model and A New Infrared Regularization

TL;DR

This paper introduces a new infrared regularization method for solving the Randall-Sundrum model with an $S^1/Z_2$ extra dimension, revealing domain-wall and anti-domain-wall structures and ensuring stability through kink boundary conditions.

Contribution

It presents a novel infrared regularization approach that yields continuous solutions and clarifies the ultraviolet-infrared relation in the Randall-Sundrum model.

Findings

Domain-wall and anti-domain-wall naturally emerge at the ends of the extra dimension.

A continuous, infrared-regularized solution is constructed as a truncated Fourier series.

The stability of the configuration is guaranteed by kink boundary conditions.

Abstract

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.