Clockwork Goldstone Bosons

TL;DR

This paper explores the clockwork mechanism's symmetry breaking patterns, light states, and realizations in 5D models, including scalar and gauge theories, revealing new parity rules and deconstructed analogues.

Contribution

It provides a detailed analysis of the clockwork mechanism's self-interactions, symmetry breaking in 5D models, and constructs novel 4D and 5D realizations including non-abelian cases.

Findings

Discovery of a parity-like selection rule in scalar clockwork models.

Realization of clockwork in 5D linear dilaton models with spontaneous symmetry breaking.

Construction of 4D deconstructed analogues of 5D gauge theories with clockwork features.

Abstract

The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states referred to as `gears'. In this paper we begin by investigating the self-interactions of these gears in a scalar clockwork model and find a parity-like selection rule at all orders in the fields. We then proceed to investigate how the clockwork mechanism can be realized in 5D linear dilaton models from the spontaneous symmetry breaking of a complex bulk scalar field. We also discuss how the clockwork mechanism is manifest in the scalar components of 5D gauge theories in the linear dilaton model, and build their 4D deconstructed analogue. Finally we discuss attempts at building both 4D and 5D realizations of a non-abelian scalar clockwork mechanism, where in the latter we consider scenarios in which the Goldstone bosons arise from 5D scalar and 5D gauge fields.