Wilson-'t Hooft operators and the theta angle

Abstract

We consider $(3+1)$-dimensional $SU(N)/{\mathbb{Z}}_N$ 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 $\theta \to \theta +2\pi$, a 't Hooft operator $T(\gamma )$ associated with a closed spatial curve $\gamma$ that winds around the compact direction undergoes a monodromy $T(\gamma )\to T^{\prime }(\gamma )$. The new 't Hooft operator $T^{\prime }(\gamma )$ transforms under large gauge transformations in the same way as the product $T(\gamma )W(\gamma )$, where $W(\gamma )$ is the Wilson operator associated with the curve $\gamma$ and the fundamental representation of SU(N).

7 pages

Cited by in corpus (1)

• BPS surface observables in six-dimensional (2,0) theory