Axion Mass from Magnetic Monopole Loops

Understand

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.