Wilson-’t Hooft operators and the theta angle

We consider (3+1)-dimensional SU(N)/ZN Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle θ → θ+2π, a ’t Hooft operator T (γ) associated with a closed spatial curve γ that winds around the compact direction undergoes a monodromy T (γ) → T (γ). The new ’t Hooft operator T (γ) transforms under large gauge transformations in the same way as the product T (γ)W (γ), where W (γ) is the Wilson operator associated with the curve γ and the fundamental representation of SU(N).