Numerical hints for dyon condensation at θ = 2π via Wilson-’t Hooft loops in SU(2) Yang-Mills theory

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