Wilson-'t Hooft operators and the theta angle

Details Wilson-'t Hooft operators and the theta angle Wilson-'t Hooft operators and the theta angle

2006-03-24

arxiv.org/abs/hep-th/0603188v1

JHEP0605:065,2006

Physics

High Energy Physics

High Energy Physics - Theory

7 pages

Scientific paper

10.1088/1126-6708/2006/05/065

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).

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