Axion Couplings in Grand Unified Theories

We show that the couplings of axions to gauge bosons are highly restricted in Grand Unified Theories where the standard model is embedded in a simple 4D gauge group. 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 unification. This implies that 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. Axions which break the unification relation between gluon and photon couplings are necessarily charged under the GUT gauge group and become heavy from perturbative mass contributions. A discovery of an axion to the left of the QCD line can rule out simple Grand Unified models. Axion searches are therefore tabletop and astrophysical probes of Grand Unification.