Line operators, vortex statistics, and Higgs versus confinement dynamics

TL;DR

This paper investigates a 2+1D lattice gauge theory with scalar fields, distinguishing Higgs and confining phases via vortex line operators and dualities, providing new analytical insights into the phase diagram.

Contribution

It introduces a gauge-invariant observable based on vortex line operators to differentiate phases and employs dualities and strong coupling expansions for analytical exploration.

Findings

Higgs and confining regimes are distinguishable by vortex line operator phases.

Dualities enable analysis of previously inaccessible parameter regimes.

Implications for the phase diagram of 2+1D gauge theories are discussed.

Abstract

We study a $2{+}1$D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken $U(1)$ $0$-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase $\Omega$ of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.