On Hierarchy, Charge Universality, and 4D Effective Theory in Randall-Sundrum Models

Abstract

We present a variant formulation of the Randall-Sundrum model which solves both the hierarchy and charge universality problems. We first critique the rationale for hierarchy solution and 4D effective interactions in the Randall-Sundrum model. We note its asymmetric treatment of matter and gravity in the warped braneworld background, leaving uncalibrated the particle scale; as well as its unconventional spatial attribution of integrated 4D effective gravity. Matter and massless gravitons both localize when branes form to warp spacetime; thus consistent accounting of induced 4D physics must track both particle and Planck scales through brane formation. We perform such self-consistent tracking in the warped Randall-Sundrum background, by treating matter as intrinsically extradimensional, on par with gravity, with a unified mass scale. We find this definite, self-consistent theory solves two major problems: the effective 4D theory shows robust hierarchy solution, and preserves charge universality. Our unified 5D field theory lies at the Planck scale; it induces an integrated 4D effective field theory with universal charges, Planck scale 4D gravity, and TeV scale matter. However, this effective field theory describes, not 4D physics on a specific brane, but 4D physics induced by an unobservably small (12 M_{Pl}^{-1}) warped extra dimension. This unified approach validates Randall-Sundrum hierarchy solution, while exemplifying a field theory whose dimensional reduction preserves charge universality.