Speaker
Description
We report a lattice study of the confinement vacuum of $SU(2)$ Yang--Mills theory at $\theta=2\pi$ using Wilson--'t~Hooft loop observables. Although Yang--Mills theories at $\theta$ and $\theta+2\pi$ are unitarily equivalent, recent developments in generalized global symmetries predict that the confining vacua at $\theta=0$ and $\theta=2\pi$ are distinguished as symmetry-protected topological states associated with the $Z_2$ one-form center symmetry. This distinction can be probed through the Wilson--'t~Hooft classification of gapped phases, where monopole and dyon condensation are characterized by different area/perimeter laws of line operators. We formulate the measurement at $\theta=2\pi$ by inserting an 't Hooft defect and evaluating the corresponding topological phase factor. To define the topological charge in the presence of the defect, we employ a one-form covariant DBW2 gradient flow, which stabilizes topological sectors and makes the reweighting factor numerically tractable. Our simulations with the Wilson plaquette action show a clear perimeter-law behavior for the dyonic loop, while the direct signal for the area law of the 't Hooft loop is statistically challenging. These results provide numerical hints for dyon condensation at $\theta=2\pi$, rather than monopole condensation, in agreement with the expected SPT structure of the confinement vacua.