Dynamics of a Stabilized Radion and Duality

TL;DR

This work develops an effective radion theory in Randall-Sundrum geometries with Goldberger-Wise stabilization, quantifying how stabilization shapes the radion mass and its couplings to Standard Model fields. It shows that a light radion arises only with mild tuning of bulk parameters or IR-brane tension, and that stabilization-induced corrections to radion couplings are generically suppressed by (m_radion/m_KK)^2, becoming potentially relevant for gluon and photon couplings. By embedding the AdS/CFT correspondence, the authors reconcile radion and dilaton results, demonstrating that bulk self-interactions of the GW field are necessary to achieve agreement between the RS radion and the CFT dilaton pictures, particularly in the IR regime. The analysis clarifies when a light radion is natural in holographic EWSB scenarios and highlights the interplay between stabilization dynamics and phenomenology at colliders.

Abstract

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.

Figures (1)

• Figure 1: 1a: The approximate solution (solid line) matches well with the BR solution (large dotted) and the OR solution (small dotted) for $\epsilon=-0.1,\,k\pi r_c=10$. We have also taken $v=0.05$ and $\alpha=-0.5$. The shaded region separates the boundary region on its right from the outer region on its left. Asymptotic matching is done in the shaded region. 1b: The approximate solution (dotted) agrees well with the exact solution (solid) for the same parameter values, and we show the agreement near the $\theta=\pi$ boundary.