A Clockwork Axion

TL;DR

This paper introduces a renormalizable scalar theory featuring a pseudo-Goldstone boson with a large field range and approximate discrete symmetry, providing a new mechanism for exponential scale separation in field theory.

Contribution

It presents a novel renormalizable model with a pseudo-Goldstone boson exhibiting large field excursions and discrete symmetry, serving as a UV completion for relaxion models.

Findings

The model achieves super-Planckian field excursions within renormalizable 4D QFT.

It demonstrates a logarithmic increase in the number of fields with Q, enabling exponential scale separation.

A supersymmetric extension and UV completions via extra dimensions are constructed.

Abstract

We present a renormalizable theory of scalars in which the low energy effective theory contains a pseudo-Goldstone Boson with a compact field space of 2{\pi} F and an approximate discrete shift symmetry Z_Q with Q>>1, yet the number of fields in the theory goes as log(Q). Such a model can serve as a UV completion to models of relaxions and is a new source of exponential scale separation in field theory. While the model is local in `theory space', it appears to not have a continuum generalization (i.e., it cannot be a deconstructed extra dimension). Our framework shows that super-Planckian field excursions can be mimicked while sticking to renormalizable four-dimensional quantum field theory. We show that a supersymmetric extension is straightforwardly obtained and we illustrate possible UV completions based on a compact extra-dimension, where all global symmetries arise accidentally as a consequence of gauge invariance and 5D locality.