Analyzing the Higgs-confinement transition with non-local operators on the lattice

TL;DR

This paper investigates the Higgs-confinement phase transition in lattice gauge theory using non-local operators, including novel approaches like the Aharonov-Bohm phase, to better understand the topological nature of the transition.

Contribution

It introduces and tests various non-local operators, including the Aharonov-Bohm phase, as order parameters for the Higgs-confinement transition in a charge-2 Abelian Higgs model.

Findings

Polyakov loop and 't Hooft loop effectively detect the transition.

The Aharonov-Bohm phase provides new insights into topological aspects.

Numerical simulations confirm the topological nature of the phase transition.

Abstract

We study non-local 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 non-local operators, such as loop and surface operators. There exist several candidates for the non-local 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.