From Soft Walls to Infrared Branes

TL;DR

This paper demonstrates how soft wall models in warped extra dimensions can be effectively described by an infrared brane, simplifying analysis and enabling better comparison with traditional Randall-Sundrum models.

Contribution

It provides a method to replace the singularity in soft wall backgrounds with an effective brane, clarifying the physics and improving analytical tractability.

Findings

Effective brane description reproduces bulk field spectra accurately.

Universal behavior near the singularity reflected in the effective brane Lagrangian.

Approximate models using Randall-Sundrum backgrounds are valid away from the singularity.

Abstract

Five dimensional warped spaces with soft walls are generalizations of the standard Randall-Sundrum compactifications, where instead of an infrared brane one has a curvature singularity (with vanishing warp factor) at finite proper distance in the bulk. We project the physics near the singularity onto a hypersurface located a small distance away from it in the bulk. This results in a completely equivalent description of the soft wall in terms of an effective infrared brane, hiding any singular point. We perform explicitly this calculation for two classes of soft wall backgrounds used in the literature. The procedure has several advantages. It separates in a clean way the physics of the soft wall from the physics of the five dimensional bulk, facilitating a more direct comparison with standard two-brane warped compactifications. Moreover, consistent soft walls show a sort of universal behavior near the singularity which is reflected in the effective brane Lagrangian. Thirdly, for many purposes, a good approximation is obtained by assuming the bulk background away from the singularity to be the usual Randall-Sundrum metric, thus making the soft wall backgrounds better analytically tractable. We check the validity of this procedure by calculating the spectrum of bulk fields and comparing it to the exact result, finding very good agreement.