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

Understand

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.