A Witten effect for global monopoles

Global monopoles can carry electric charge even when the scalar field that forms them is neutral. We show that a CP-odd operator in the Goldstone effective theory, typically discarded as a total derivative, gives them an electric charge $Q=-Cn$, with $C$ its Wilson coefficient and $n$ the winding number. This is a Witten effect on a global defect, generated by a mixed $\theta$-term between electromagnetism and a composite connection built from the Goldstone fields. The same group theory condition that allows the operator also guarantees the existence of monopoles. We also give a fermionic UV completion and determine the coefficient by matching the Goldstone-Wilczek current.