Axion Mass from Magnetic Monopole Loops

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 non-Abelian instantons and Euclidean brans 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.

Automated summary

The research shows that axions interacting with Abelian gauge fields acquire potential energy from magnetic monopoles. This axion potential can be understood as related to both instanton effects and Witten effect. It is also discussed how this potential is important in determining dark matter relic abundance in specific scenarios.