A stable hierarchy from Casimir forces and the holographic interpretation

TL;DR

The paper addresses stabilizing the radion in the Randall-Sundrum model by quantum Casimir effects of bulk gauge fields, which generate a radion potential with a distinctive $V(a) \sim k^4 a^4/\ln a$ dependence that can fix the warp factor $a$ without fine-tuning. Using AdS/CFT, the authors relate these logarithmic terms to the running of gauge couplings in a 4D dual CFT, elucidating how bulk gauge dynamics produce a naturally small $a$. They compute the one-loop radion potential from the KK spectrum and show that, with appropriate brane terms, a stable minimum exists giving the observed hierarchical separation of scales and a TeV-scale radion mass. This mechanism offers a Casimir-energy alternative to the Goldberger-Wise stabilization and highlights a holographic interpretation where radion stabilization mirrors gauge-coupling running in the dual 4D theory.

Abstract

We show that in the Randall-Sundrum model the Casimir energy of bulk gauge fields (or any of their supersymmetric relatives) has contributions that depend logarithmically on the radion. These contributions satisfactorily stabilize the radion, generating a large hierarchy of scales without fine-tuning. The logarithmic behaviour can be understood, in a 4D holographic description, as the running of gauge couplings with the infrared cut-off scale.

Figures (2)

• Figure 1: Correction to the mass of $V$.
• Figure 2: Correction to the mass of $S$.