The Monodromic Axion-Photon Coupling

Understand

We consider the general form of the axion coupling to photons in the axion-Maxwell theory.

• On general grounds this coupling takes the form of a monodromic function of the axion, which we call $g(a)$, multiplying the Chern-Pontryagin density $F \widetilde{F}$ of the photon.
• We show that the non-linearity of $g(a)$ is a spurion for the shift symmetry of the axion.
• In this context, when $g(a) \neq \mathbb{Z}a$, the linearized coupling of the axion $g'(a)$ is not quantized and there is a correlated mass term for the axion.