Quadratic Axion Couplings in String Theory

Abstract

Axions and axion-like particles are a compelling candidate for physics beyond the standard model. While many axion searches are focused on the linear coupling to photons $θF \tilde{F}$, the possibility of a quadratic coupling to the electromagnetic kinetic term, $θ^2 F^2$, leads to novel phenomenology and new opportunities for testing axion-like particles. In this work we propose mechanisms for generating this coupling in string theory, which can be broadly classified as classical, perturbative, and non-perturbative. In benchmark examples, we find that both perturbative and non-perturbative quantum contributions such as instantons lead to couplings that are suppressed, $g \ll 1$ in units of $1/f^2$ where $f$ is axion decay constant, though easily larger than analogous coupling of the QCD axion that is generated through loops of charged pions. These analyses suggest that quadratic axion couplings to gauge fields are ubiquitous in string theory, and should be taken seriously as a probe of the string theory axiverse, both of string theory candidates for dynamical axions, such as dark matter or dark energy, and for spectroscopy of the string theory axiverse.