The Dilaton, the Radion and Duality

Abstract

In this dissertation, scenarios where strong conformal dynamics constitutes the ultraviolet completion of the physics that drives electroweak symmetry breaking are considered. It is shown that in theories where the operator responsible for the breaking of conformal symmetry is close to marginal at the breaking scale, the dilaton mass can naturally lie below the scale of the strong dynamics. However, in general this condition is not satisfied in the scenarios of interest for electroweak symmetry breaking, and so the presence of a light dilaton in these theories is associated with mild tuning. The effective theory of the light dilaton is constructed in this framework, and the form of its couplings to Standard Model states are determined. It is shown that corrections to the form of the dilaton interactions arising from conformal symmetry violating effects are suppressed by the square of the ratio of the dilaton mass to the strong coupling scale, and are under good theoretical control. These corrections are generally subleading, except in the case of dilaton couplings to marginal operators, when symmetry violating effects can sometimes dominate. Phenomenological implications of these results are investigated for models of technicolor, and for models of the Higgs as a pseudo-Nambu-Goldstone boson, that involve strong conformal dynamics in the ultraviolet. Using AdS/CFT correspondence, a holographic realization of this scenario is obtained by constructing the effective theory of the graviscalar radion in the Randall-Sundrum models, taking stabilization into account. The conditions under which the radion can remain light are explored, and the corrections to its couplings to Standard Model (SM) states localized on the visible brane are determined. It is shown that in the theories of interest for electroweak symmetry breaking that have a holographic dual, the presence of a light radion requires mild tuning. Corrections to the form of the radion coupling to SM states arising from effects associated with brane stabilization are also calculated. These corrections scale as the square of the ratio of the radion mass to the Kaluza-Klein scale, and are generally subleading, except in the case of gluons and photon, when they can sometimes dominate. These results are in agreement with and lend robustness to the conclusions for the dilaton.