Global Structure, Non-Invertible PQ Symmetry, and the DFSZ Domain Wall Problem

TL;DR

This paper explores how the global structure of symmetry groups influences the axion domain wall problem in DFSZ models, proposing solutions via non-invertible symmetries and potential gravitational wave signals.

Contribution

It reveals the role of global group structure and non-invertible symmetries in addressing the DFSZ domain wall problem and suggests UV completions and observable signatures.

Findings

Global structure affects the nature of the domain wall problem in DFSZ models.

Non-invertible chiral symmetries can stabilize domain walls in quark flavor models.

Potential gravitational wave signals from axion domain wall annihilation are discussed.

Abstract

In recent years it has become increasingly clear that the previously overlooked ``global structure'' of symmetry groups can encode significant theoretical structure and, more importantly, have substantial phenomenological implications. With this in mind we re-examine the DFSZ axion, which suffers from a domain wall problem due to the Standard Model generation structure. We show that global structure $(G_{\text{EW}} \times U(1)_{\text{PQ}})/\mathbb{Z}_2$ acting between the Peccei-Quinn symmetry and the electroweak gauge group plays a crucial role in determining the precise nature of the domain wall problem, which has important implications in both cubic and quartic DFSZ. We then demonstrate that the stability of the domain walls is enforced by a non-invertible chiral symmetry in quark flavor $Z'$ models which have additional global structure $(SU(3)_C \times G_F)/\mathbb{Z}_3$ acting between the color and the gauged quark flavor groups. The strategy of Non-invertible Naturalness then leads us to UV theories that resolve the domain wall problem through small-instanton-induced breaking of non-invertible symmetries. Finally, we sketch potential gravitational wave signatures arising from the annihilation of axion domain walls. Our work illustrates the importance of considerations of global structure in realistic models of particle physics.