Axion Domain Walls, Small Instantons, and Non-Invertible Symmetry Breaking

TL;DR

This paper explores how non-invertible symmetries and small instantons influence axion domain walls, offering potential solutions to the domain wall problem and implications for observable signals like gravitational waves.

Contribution

It introduces a framework connecting non-invertible symmetries, small instantons, and axion physics, applying these ideas to the Standard Model and proposing UV completions that address the domain wall issue.

Findings

Small instantons can lift vacuum degeneracy, breaking non-invertible symmetries.

Different global structures of the Standard Model lead to distinct axion coupling rules.

A UV embedding can potentially solve the axion domain wall problem.

Abstract

Non-invertible global symmetry often predicts degeneracy in axion potentials and carries important information about the global form of the gauge group. When these symmetries are spontaneously broken they can lead to the formation of stable axion domain wall networks which support topological degrees of freedom on their worldvolume. Such non-invertible symmetries can be broken by embedding into appropriate larger UV gauge groups where small instanton contributions lift the vacuum degeneracy, and provide a possible solution to the domain wall problem. We explain these ideas in simple illustrative examples and then apply them to the Standard Model, whose gauge algebra and matter content are consistent with several possible global structures. Each possible global structure leads to different selection rules on the axion couplings, and various UV completions of the Standard Model lead to more specific relations. As a proof of principle, we also present an example of a UV embedding of the Standard Model which can solve the axion domain wall problem. The formation and annihilation of the long-lived axion domain walls can lead to observables, such as gravitational wave signals. Observing such signals, in combination with the axion coupling measurements, can provide valuable insight into the global structure of the Standard Model, as well as its UV completion.