Analyzing the Higgs–Confinement Transition with Nonlocal Operators on the Lattice

Abstract We study nonlocal operators for analyzing the Higgs–confinement phase transition in lattice gauge theory. Since the nature of the Higgs–confinement phase transition is topological, its order parameter is the expectation value of nonlocal operators, such as loop and surface operators. There exist several candidates for the nonlocal operators. Adopting the charge-2 Abelian Higgs model, we test numerical simulation of conventional ones, the Polyakov loop and the ’t Hooft loop, and an unconventional one, the Aharonov–Bohm phase defined by the Wilson loop wrapping around a vortex line.