Quantization of Axion-Gauge Couplings and Non-Invertible Higher Symmetries

TL;DR

This paper establishes model-independent quantization conditions for axion couplings to the Standard Model, explores implications for axion models and global symmetries, and derives bounds on related topological objects.

Contribution

It provides new quantization conditions for axion couplings and reveals non-invertible symmetries affecting axion model constraints and topological defect bounds.

Findings

Quantization conditions restrict axion couplings to specific gauge group forms.

Models with certain coupling ratios face the axion domain wall problem.

Universal bounds on axion string tension and monopole mass are derived.

Abstract

We derive model-independent quantization conditions on the axion couplings (sometimes known as the anomaly coefficients) to the Standard Model gauge group $[SU(3)\times SU(2)\times U(1)_Y]/\mathbb{Z}_q$ with $q=1,2,3,6$. Using these quantization conditions, we prove that any QCD axion model to the right of the $E/N=8/3$ line on the $|g_{a\gamma\gamma}|$-$m_a$ plot must necessarily face the axion domain wall problem in a post-inflationary scenario. We further demonstrate the higher-group and non-invertible global symmetries in the Standard Model coupled to a single axion. These generalized global symmetries lead to universal bounds on the axion string tension and the monopole mass. If the axion were discovered in the future, our quantization conditions could be used to constrain the global form of the Standard Model gauge group.