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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 concretelywithin higher-dimensional effective field theory. Matching theories withdifferent radii leads to running hidden brane couplings. The hidden braneLagrangian consists of four-dimensional local operators constructed from theinduced value of the bulk fields on the brane. We find hidden Lagrangians whichare non-trivial fixed points of the RG flow. Calculations in RS1 can be greatlysimplified by ``running down'' the effective theory to a small radius. Wedemonstrate these simplifications by studying the Goldberger-Wise stabilizationmechanism. In this paper, we focus on the classical and tree-level quantumfield theory of bulk scalar fields, which demonstrates the essential featuresof the RG in the simplest context.Comment: 16 pages, 2 figure

Running with the radius in RS1