# Disassembling the Clockwork Mechanism

## TL;DR

This paper critically examines the clockwork mechanism, highlighting its limitations to abelian theories and clarifying that it cannot be realized solely through geometric effects in extra dimensions.

## Contribution

It demonstrates that clockwork is inherently abelian and cannot be implemented in non-abelian theories or purely geometric extra-dimensional models.

## Key findings

- Clockwork is an intrinsically abelian phenomenon.
- Non-abelian theories like Yang-Mills do not support clockwork.
- Clockwork can be realized through zero mode localization in extra dimensions.

## Abstract

The clockwork mechanism is a means of naturally generating exponential hierarchies in theories without significant hierarchies among fundamental parameters. We emphasize the role of interactions in the clockwork mechanism, demonstrating that clockwork is an intrinsically abelian phenomenon precluded in non-abelian theories such as Yang-Mills, non-linear sigma models, and gravity. We also show that clockwork is not realized in extra-dimensional theories through purely geometric effects, but may be generated by appropriate localization of zero modes.