Exact accidental U(1) symmetries for the axion

TL;DR

This paper explores gauge groups that naturally produce exact Peccei-Quinn symmetries, offering solutions to the axion quality problem and enabling accidental symmetries like the clockwork, with a toy model illustrating an invisible axion.

Contribution

It introduces a class of gauge groups that automatically generate exact Peccei-Quinn symmetries and solves the axion quality problem at all operator dimensions.

Findings

Gauge groups can enforce exact accidental U(1) symmetries.

A model demonstrates an invisible axion from single symmetry breaking.

The approach addresses the axion quality problem comprehensively.

Abstract

We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries.