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arXiv · 2606.13428

Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory

Hiromasa Watanabe·Issaku Kanamori·Okuto Morikawa·Yuki Nagai·Yuya Tanizaki·Akio Tomiya
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Abstract

Yang-Mills theories at $\theta$ and $\theta+2\pi$ are unitarily equivalent, but their $2\pi$ periodicity has a nontrivial realization. Recent developments in generalized symmetries rigorously prove that confinement vacua at $\theta=0$ and $2\pi$ should belong to different symmetry-protected topological (SPT) states with the $1$-form center symmetry. For its examination, we measure the Wilson-'t Hooft loop operators at $\theta=2\pi$ for the $SU(2)$ Wilson lattice gauge action and discuss their long-distance behaviors. This requires us to identify the gauge topological charge in the presence of defects, and we employ the $1$-form covariant DBW2 gradient flow to smear lattice gauge fields. We find a clear perimeter-law signal for the dyonic Wilson-'t Hooft loop at $\theta=2\pi$, providing numerical evidence in the pure $SU(2)$ Yang-Mills theory for the theoretically expected dyon condensation at $\theta=2\pi$.

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Hiromasa Watanabe, Issaku Kanamori, Okuto Morikawa, Yuki Nagai, Yuya Tanizaki, Akio Tomiya. 2026-06-11. Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory. https://arxiv.org/abs/2606.13428

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