A systematic study of the radion in the compact Randall-Sundrum model

TL;DR

This paper provides a comprehensive analysis of the radion field in the Randall-Sundrum model, establishing its unambiguous identification, deriving the effective action, and exploring its spectrum and couplings.

Contribution

It offers a systematic Lagrangian formulation of the radion, including all orders in the field, and analyzes the effective 4D theory and classical solutions.

Findings

Radion can be unambiguously identified using symmetry properties.

Derived the radion action to all orders in the field.

Analyzed the spectrum and couplings of the effective 4D theory.

Abstract

We systematically study the question of identification and consistent inclusion of the radion, within the Lagrangian approach, in a two brane Randall-Sundrum model. Exploiting the symmetry properties of the theory, we show how the radion can be identified unambiguously and give the action to all orders in the radion field and the metric. Using the background field method, we expand the theory to quadratic orders in the fields. We show that the most general classical solutions, for the induced metric on the branes in the case of a constant radion and a factorizable 4D metric, correspond to Einstein spaces. We discuss extensively the diagonalization of the quadratic action. Furthermore, we obtain the 4-dimensional effective theory from this and study the question of the spectrum as well as the couplings in these theories.