Study of compact abelian lattice gauge theories

TL;DR

This review discusses lattice studies of compact abelian gauge theories, highlighting their potential to define continuum or effective theories with notable nonperturbative phenomena such as confinement and mass generation.

Contribution

It provides an overview of lattice investigations into pure compact QED and U(1) theories with matter fields, emphasizing their nonperturbative properties and possible continuum limits.

Findings

Evidence of confinement in lattice models

Indications of dynamical mass generation

Potential continuum field theories emerging from lattice studies

Abstract

This is a review, intended for lattice nonspecialists, of the studies of the compact abelian gauge theories on the lattice performed by the Aachen lattice field theory group. We discuss in particular the pure compact QED and a U(1) lattice gauge theory with charged scalar and fermion fields in four and three dimensions. Our data indicate that these lattice theories might define some continuum field theories, or at least effective field theories with remarkable nonperturbative properties like confinement and dynamical mass generation.