Compact QED: the photon propagator, confinement and positivity violation for the pure gauge theory

TL;DR

This paper investigates the photon propagator in pure gauge theory using lattice simulations, revealing confinement-related features, a mass gap linked to monopoles, and positivity violation in the confined phase, with a transition to free-field behavior in the deconfined phase.

Contribution

It provides a detailed lattice analysis of the photon propagator, highlighting confinement effects, mass gap origin, and spectral positivity violation, advancing understanding of gauge theory phases.

Findings

Confined phase exhibits linearly growing potential and positivity violation.

Mass gap is related to monopole presence.

Deconfined phase approaches free-field behavior in large lattices.

Abstract

The lattice Landau gauge photon propagator for the pure gauge theory is revisited using large lattices. For the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function violates positivity. In the deconfined phase, our simulations suggest that a free field theory is recovered in the thermodynamic limit.