Running with the radius in RS1

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 nontrivial 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