Axion Mass from Magnetic Monopole Loops

TL;DR

This paper demonstrates that magnetic monopole loops induce an axion potential via the Witten effect, with implications for dark matter relic abundance in models with hidden abelian sectors.

Contribution

It introduces a novel mechanism for axion potential generation from monopole loops, connecting monopole physics with axion cosmology and dark matter.

Findings

Monopole loops generate an axion potential through the Witten effect.

The potential vanishes with massless charged fermions, ensuring consistency.

The effect is robust against higher-derivative corrections.

Abstract

We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an abelian gauge group, monopoles, and axions.