Axion Couplings as UV Probes

The couplings of axions to gauge bosons are highly restricted in Grand Unified Theories and heterotic string models. The topological nature of these couplings allows them to be matched from the UV to the IR, and the ratio of the anomaly with photons and gluons for any axion is fixed by UV physics. This implies that in unified theories there is a single axion, the QCD axion, with an anomalous coupling to photons. Other light axion-like particles can couple to photons by mixing through the QCD axion portal and lie to the right of the QCD line in the mass-coupling plane. Similar results hold both in heterotic string theory and orbifold GUTs. A discovery of an axion to the left of the QCD line can rule out simple Grand Unified models and some heterotic models. Axion experiments are therefore experimental probes of Grand Unification and string theory.