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Dynamics of a Stabilized Radion and Duality

We construct the effective theory of the graviscalar radion in the Randall-Sundrum scenario, taking into account effects arising from the stabilization of the extra dimension through the Goldberger-Wise mechanism. We explore the conditions under which the radion can remain light, and determine the corrections to its couplings to Standard Model (SM) states when the effects of stabilization are taken into account. We show that in the theories of interest for electroweak symmetry breaking that have a holographic dual, the presence of a light radion in the spectrum is not a robust prediction of the framework, but is in fact associated with mild tuning. We find that corrections to the form of the radion couplings to Standard Model particles arising from effects associated with brane stabilization are suppressed by the square of the ratio of the radion mass to the Kaluza-Klein scale. These corrections are small in theories where the radion is light, and are generally subleading, except in the case of couplings to the SM gluons and photon, when they can sometimes dominate. The AdS/CFT correspondence relates the radion in Randall-Sundrum models to the dilaton in theories where a strongly coupled conformal symmetry is spontaneously broken. We show that the discrepancies in the literature between the results for the dilaton and the radion can be traced to the omission of self-interaction terms that would otherwise dominate the potential for the Goldberger-Wise scalar near the infrared brane. In the dual picture, this corresponds to neglecting the corrections to the scaling behavior of the operator that breaks conformal symmetry when it grows large. With the inclusion of these self-interaction terms, we find good agreement between the results on the two sides of the correspondence.