[2606.13428] Numerical Hints for Dyon Condensation at $θ=2π$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory

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High Energy Physics - Lattice

arXiv:2606.13428 (hep-lat)

[Submitted on 11 Jun 2026]

Title:Numerical Hints for Dyon Condensation at $θ=2π$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory

Authors:Hiromasa Watanabe, Issaku Kanamori, Okuto Morikawa, Yuki Nagai, Yuya Tanizaki, Akio Tomiya<br>View a PDF of the paper titled Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory, by Hiromasa Watanabe and 5 other authors

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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 global symmetries show 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 then obtain numerical evidence consistent with dyon condensation at $\theta=2\pi$, rather than monopole condensation, as theoretically predicted.

Comments:<br>1+28 pages, 15 figures, 2 tables

Subjects:

High Energy Physics - Lattice (hep-lat); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

Report number:<br>YITP-26-11, RIKEN-iTHEMS-Report-26

Cite as:<br>arXiv:2606.13428 [hep-lat]

(or<br>arXiv:2606.13428v1 [hep-lat] for this version)

https://doi.org/10.48550/arXiv.2606.13428

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Hiromasa Watanabe [view email]<br>[v1]<br>Thu, 11 Jun 2026 14:56:39 UTC (898 KB)

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