Fermions, scalars and Randall-Sundrum gravity on domain-wall branes

TL;DR

This paper investigates how fermions and scalars localize on a domain-wall brane in a Randall-Sundrum model, showing the presence of normalizable continuum modes and the decoupling of these modes at low energies, leading to effective four-dimensional physics.

Contribution

It provides a detailed analysis of matter field spectra in a smoothed domain-wall Randall-Sundrum model, including the behavior of bound states and resonances, and demonstrates low-energy decoupling of continuum modes.

Findings

Scalar and fermion fields have a continuum of normalizable modes starting at zero mass.

Discrete bound modes become resonances in the continuum, with off-resonant modes suppressed on the brane.

Continuum modes decouple at low energies, resulting in effective four-dimensional physics.

Abstract

We analyse the general features of localisation of fermions and scalars in smoothed field-theoretical versions of the type 2 Randall- Sundrum braneworld model. A scalar field domain-wall forms the brane, inducing warped gravity, and we study the mass spectra of the matter fields in the dimensionally reduced theory. We demonstrate explicitly that both scalar and fermion fields exhibit a continuum of properly normalisable modes starting at zero mass. If discrete bound modes are present in the gravity-free case, these become resonances in the continuum, while off-resonant modes are highly suppressed on the brane. We describe briefly how another scalar field can be used to break a symmetry on the domain-wall while leaving it unbroken far from the wall, as has already been done in the flat space case. Finally we present numerical calculations for a toy model which demonstrates the decoupling of continuum modes at low energies, so the theory becomes four dimensional.