General Continuum Clockwork

TL;DR

This paper explores a generalized 5D linear dilaton model to realize continuum clockwork mechanisms, analyzing KK spectra and couplings, and discussing the limitations compared to discrete clockwork.

Contribution

It introduces a flexible 5D model framework for continuum clockwork, allowing independent control of volume, warping, and localization parameters.

Findings

KK spectra vary with volume, warping, and localization parameters.

Zero mode and KK mode couplings depend on model parameters.

Continuum clockwork has limitations compared to discrete versions.

Abstract

The continuum clockwork is an extra-dimensional set-up to realize certain features of the clockwork mechanism generating exponentially suppressed or hierarchical couplings of light particles. We study the continuum clockwork in a general scheme in which large volume, warped geometry, and localization of zero modes in extra dimension are described by independent parameters. For this, we propose a generalized 5-dimensional linear dilaton model which can realize such set-up as a solution of the model, and examine the KK spectrum and the couplings of zero modes and massive KK modes to boundary-localized operators for the bulk graviton, Abelian gauge bosons and periodic scalar fields. We discuss how those KK spectra and couplings vary as a function of the volume, warping and localization parameters, and highlight the behavior in the parameter region corresponding to the clockwork limit. We discuss also the field range of 4-dimensional axions originating from either 5-dimensional periodic scalar field or the 5-th component of an Abelian gauge field, and comment on the limitations of continuum clockwork compared to the discrete clockwork.