The Clockwork Supergravity

TL;DR

This paper demonstrates that minimal five-dimensional N=2 gauged supergravity naturally encodes the clockwork mechanism, producing a power-law hierarchy and connecting to models like Randall-Sundrum within a supersymmetric framework.

Contribution

It shows how the minimal supergravity setup can realize the clockwork mechanism with a scalar field, unifying various models and analyzing the hierarchy generated.

Findings

The hierarchy is power-law, not exponential.

The model preserves N=1 supersymmetry on boundaries.

The KK spectrum depends logarithmically on the compactification radius.

Abstract

We show that the minimal D = 5, N = 2 gauged supergravity set-up may encode naturally the recently proposed clockwork mechanism. The minimal embedding requires one vector multiplet in addition to the supergravity multiplet and the clockwork scalar is identified with the scalar in the vector multiplet. The scalar has a two-parameter potential and it can accommodate the clockwork, the Randall-Sundrum and a no-scale model with a flat potential, depending on the values of the parameters. The continuous clockwork background breaks half of the original supersymmetries, leaving a D = 4, N = 1 theory on the boundaries. We also show that the generated hierarchy by the clockwork is not exponential but rather power law. The reason is that four-dimensional Planck scale has a power-law dependence on the compactification radius, whereas the corresponding KK spectrum depends on the logarithm of the latter.