The Monodromic Axion-Photon Coupling

TL;DR

This paper explores the general form of axion-photon couplings in axion-Maxwell theory, revealing their monodromic nature, relation to shift symmetry, and implications for axion potentials across various models.

Contribution

It introduces the concept of monodromic axion-photon coupling functions and derives their general form for different axion scenarios, linking coupling non-linearity to shift symmetry breaking.

Findings

g(a) is a monodromic function multiplying F~F

Non-linearity of g(a) indicates shift symmetry breaking

Singularities in g(a) correspond to potential cusps

Abstract

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. Singularities in $g(a)$ due to the fast rearrangement of degrees of freedom are shown to have corresponding cusps and singularities in the axion potential. We derive the general form of $g(a)$ for the QCD axion, axions with perturbatively broken shift symmetries and axions descending from extra dimensions. In all cases, we show that there is a uniform general form of the monodromic function $g(a)$ and it is connected to the axion potential.