Hierarchy Stabilization in Warped Supersymmetry

TL;DR

This work provides a calculable framework for stabilizing the radius modulus in a supersymmetric RS1 setup by coupling 5D supergravity to bulk and boundary SYM sectors, whose nonperturbative dynamics generate a stabilizing potential for the radion. A carefully constructed 4D effective theory, written in off-shell N=1 supergravity, captures the radion and graviphoton moduli and their interactions with visible and hidden sectors, with the warp factor encoded in the ω = φ e^{-k T} combination. The authors derive explicit minima for the radion-dependent potential, show large warp factors arise naturally when |c| ≪ |a|, and ensure a vanishing 4D cosmological constant through SUSY breaking on the hidden brane, yielding radion and gravitino mass scales tied to the SUSY-breaking sector. Overall, the paper offers a complete, SUSY-consistent mechanism for generating large hierarchies in warped compactifications and provides tools potentially extendable to string/M-theory contexts.

Abstract

We show that exponentially large warp factor hierarchies can be dynamically generated in supersymmetric compactifications. The compactification we consider is the supersymmetric extension of the Randall-Sundrum model. The crucial issue is the stabilization of the radius modulus for large warp factor. The stabilization sector we employ is very simple, consisting of two pure Yang--Mills sectors, one in the bulk and the other localized on a brane. The only fine-tuning required in our model is the cancellation of the cosmological constant, achieved by balancing the stabilization energy against supersymmetry breaking effects. Exponentially large warp factors arise naturally, with no very large or small input parameters. To perform the analysis, we derive the 4-dimensional effective theory for the supersymmetric Randall-Sundrum model, with a careful treatment of the radius modulus. The manifestly (off-shell) supersymmetric form of this effective lagrangian allows a straightforward and systematic treatment of the non-perturbative dynamics of the stabilization sector.