Running with the Radius in RS1

TL;DR

This paper develops a renormalization group formalism for the Randall-Sundrum model with a variable compactification radius, simplifying calculations and analyzing fixed points within a higher-dimensional effective field theory framework.

Contribution

It introduces a concrete RG approach for RS1, deriving hidden brane couplings and fixed points, and demonstrates simplifications in calculations via radius running.

Findings

Identification of non-trivial fixed points in hidden brane Lagrangians

Simplification of RS1 calculations by running to small radius

Application to Goldberger-Wise stabilization mechanism

Abstract

We derive a renormalization group formalism for the Randall-Sundrum scenario, where the renormalization scale is set by a floating compactification radius. While inspired by the AdS/CFT conjecture, our results are derived concretely within higher-dimensional effective field theory. Matching theories with different radii leads to running hidden brane couplings. The hidden brane Lagrangian consists of four-dimensional local operators constructed from the induced value of the bulk fields on the brane. We find hidden Lagrangians which are non-trivial fixed points of the RG flow. Calculations in RS1 can be greatly simplified by ``running down'' the effective theory to a small radius. We demonstrate these simplifications by studying the Goldberger-Wise stabilization mechanism. In this paper, we focus on the classical and tree-level quantum field theory of bulk scalar fields, which demonstrates the essential features of the RG in the simplest context.