String Breaking and Z(2) Local Symmetry in the 3D Georgi-Glashow model

TL;DR

This paper analyzes the 3D Georgi-Glashow model in the London limit, deriving a Z(N) symmetry gauge and discussing string breaking due to dynamical quarks, with implications for Wilson loops and lattice observations.

Contribution

It introduces a dual approach to derive the gauging of Z(N) symmetry in the effective vortex theory for both bosonic and fermionic matter in the model.

Findings

Derivation of Z(N) symmetry gauging in the effective vortex theory.

Representation of Wilson loops showing string breaking.

Confirmation of perimeter law behavior due to dynamical quark pairs.

Abstract

In this work, we consider the London limit of the (2+1)D Georgi-Glashow model with dynamical quarks. Following Polyakov's monopole plasma approach and using dual methods to treat the relevant matter sector, we derive in a clear and straightforward manner the recently proposed gauging of the discrete Z(N) symmetry of the associated effective vortex theory. Our procedure applies to bosonic as well as to fermionic matter, enabling to derive a useful representation for the Wilson loop and discuss string breaking, due to the creation of dynamical quark-antiquark pairs. This phenomenon corresponds to a perimeter law, a behavior that has been already observed in the lattice.