The fate of the zero mode of the five-dimensional kink in the presence of gravity

TL;DR

This paper studies how gravity affects the translational zero-mode of a five-dimensional domain wall, revealing a resonance that persists as a remnant of the zero-mode and depends mainly on the space-time geometry.

Contribution

It demonstrates that gravity transforms the zero-mode into a resonance whose properties depend primarily on the space-time geometry, not on the wall's internal structure.

Findings

Identifies a wide resonance as a remnant of the zero-mode in gravitating domain walls.

Shows the resonance parameters depend mainly on the space-time geometry when the wall is thin.

Ensures continuous physical quantities change as the Planck mass varies.

Abstract

We investigate what becomes of the translational zero-mode of a five-dimensional domain wall in the presence of gravity, studying the scalar perturbations of a thick gravitating domain wall with AdS asymptotics and a well-defined zero-gravity limit. Our analysis reveals the presence of a wide resonance which can be seen as a remnant of the translational zero-mode present in the domain wall in the absence of gravity and which ensures a continuous change of the physical quantities (such as e.g. static potential between sources) when the Planck mass is sent to infinity. Provided that the thickness of the wall is much smaller than the AdS radius of the space-time, the parameters of this resonance do not depend on details of the domain wall's structure, but solely on the geometry of the space-time.