A new way of calculating the effective potential for a light radion

TL;DR

This paper introduces a rigorous method for calculating the radion effective potential in Randall-Sundrum models, improving accuracy over previous heuristic approaches and providing new computational techniques.

Contribution

The authors define a precise, field-theoretic prescription for radion potential calculation using the interpolating field method, clarifying ambiguities in prior heuristic methods.

Findings

Confirmed the validity of previous heuristic prescriptions

Developed new, more efficient calculation methods

Showed significant discrepancies in old methods for strong back-reaction models

Abstract

We address again the old problem of calculating the radion effective potential in Randall-Sundrum scenarios, with the Goldberger-Wise stabilization mechanism. Various prescriptions have been used in the literature, most of them based on heuristic derivations and then applied in some approximations. We define rigorously a light radion 4D effective action by using the interpolating field method. For a given choice of the interpolating field, defined as a functional of 5D fields, the radion effective action is uniquely defined by the procedure of integrating out the other fields, with the constrained 5D equations of motion always satisfied with help of the Lagrange multipliers. Thus, for a given choice of the interpolating fields we obtain a precise prescription for calculating the effective potential. Different choices of the interpolating fields give different prescriptions but in most cases very similar effective potentials. We confirm the correctness of one prescription used so far on a more heuristic basis and also find several new, much more economical, ways of calculating the radion effective potential. Our general considerations are illustrated by several numerical examples. It is shown that in some cases the old methods, especially in models with strong back-reaction, give results which are off even by orders of magnitude. Thus, our results are important e.g. for estimation of critical temperature in phase transitions.