Dyon Condensation at $\theta =2\pi$ from Wilson-'t Hooft Loops in Yang-Mills Theory

Although Yang–Mills theories at $\theta$ and $\theta +2\pi$ are physically equivalent, their periodicity is realized nontrivially in the presence of a background field for the $1$-form center symmetry. The confining vacua at $\theta =0$ and $2\pi$ are therefore expected to have distinct symmetry-protected topological labels. We test this expectation in $SU(2)$ lattice Yang–Mills theory by measuring 't~Hooft and dyonic Wilson–'t~Hooft loops at $\theta =2\pi$. A $1$-form-covariant DBW2 flow makes the global reweighting factor numerically benign while retaining the physical non-integer topological charge in a defect ensemble. The dyonic loop exhibits a clear perimeter-law plateau on two lattice volumes. The direct 't~Hooft-loop signal is noise-limited but has the magnitude and distance dependence expected for an area law. Taken together with the Wilson–'t~Hooft classification, these results provide numerical evidence for the dyonic oblique-confinement pattern at $\theta =2\pi$. This talk is based on our recent paper (arXiv:2606.13428).