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

Abstract

Yang-Mills theories at θ and θ+2π are unitarily equivalent, but their 2π periodicity has a nontrivial realization. Recent developments in generalized symmetries rigorously prove that confinement vacua at θ=0 and 2π 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 θ=2π 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 θ=2π, providing numerical evidence in the pure SU(2) Yang-Mills theory for the theoretically expected dyon condensation at θ=2π.

Dyon Condensation at θ=2π from Wilson-'t Hooft Loops in Yang-Mills Theory
Hiromasa Watanabe, Issaku Kanamori, Okuto Morikawa +3
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BibTeX RIS

BibTeX

@misc{watanabe2026numerical,
  title = {{Numerical Hints for Dyon Condensation at $θ=2π$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory}},
  author = {Hiromasa Watanabe and Issaku Kanamori and Okuto Morikawa and Yuki Nagai and Yuya Tanizaki and Akio Tomiya},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.13428},
  eprint = {2606.13428},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.13428},
}

RIS

TY  - UNPB
TI  - Numerical Hints for Dyon Condensation at θ=2π via Wilson-'t Hooft Loops in SU(2) Yang-Mills Theory
AU  - Hiromasa Watanabe
AU  - Issaku Kanamori
AU  - Okuto Morikawa
AU  - Yuki Nagai
AU  - Yuya Tanizaki
AU  - Akio Tomiya
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2606.13428
UR  - https://arxiv.org/abs/2606.13428
AB  - Yang-Mills theories at θ and θ+2π are unitarily equivalent, but their 2π periodicity has a nontrivial realization. Recent developments in generalized symmetries rigorously prove that confinement vacua at θ=0 and 2π 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 θ=2π 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 θ=2π, providing numerical evidence in the pure SU(2) Yang-Mills theory for the theoretically expected dyon condensation at θ=2π.
ER  -

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