Speaker
Description
Gradient flow provides a practical framework for defining and investigating gauge topology on the lattice. At finite lattice spacing, however, flow at large flow time may cause topological objects to shrink and eventually disappear, altering the identification of topological sectors. We present a systematic study of long-time gradient flow in $SU(2)$ and $SU(3)$ Yang–Mills theories, comparing the Wilson, tree-level Symanzik, Iwasaki, and DBW2 flow actions. We examine how the choice of flow action affects the convergence of the gluonic topological charge toward integer values, its stability at large flow time, its agreement with the overlap Dirac index, and its behavior toward the continuum limit.
We then discuss an application of gradient flow to Wilson–’t Hooft loop observables at $\theta=2\pi$. In the presence of an ’t Hooft loop, the topological charge is not necessarily integer quantized, and its noninteger part is relevant to the long-distance behavior of the loop. Using a 1-form-covariant DBW2 flow, we investigate the area- and perimeter-law behaviors of ’t Hooft and dyonic loops and compare them with the Wilson–’t Hooft classification. These studies highlight the role of lattice gauge topology both in identifying topological sectors and in characterizing the long-distance structure of the theory.