The Invariant Fermion Correlator in the Schwinger Model on the Torus

TL;DR

This paper constructs a gauge invariant fermion correlator in the Schwinger model on a torus, revealing its behavior at different temperatures and the role of merons, with implications for higher-dimensional theories.

Contribution

It introduces a gauge invariant fermion correlator in the Schwinger model on the torus and analyzes its temperature-dependent behavior and underlying topological structures.

Findings

Correlator decays with Coulomb energy at zero temperature

Screening mass approaches πT/2 at high temperature

High-temperature behavior involves localized merons

Abstract

We construct the gauge invariant fermion correlator in the Schwinger model on the torus. At zero temperature, this correlator falls off with a rate given by the Coulomb energy of an infinitely heavy charge. At high temperature, the screening mass approaches $\pi T/2$, and this in the presence of a mass gap. The fractional Matsubara frequency arises from the action of a pair of induced merons at high temperature that are localized over a range on the order of the meson Compton wavelength $1/m=\sqrt{\pi}/g$. We discuss the quenched approximation in this model, and comment on the possible relevance of some of these results to higher dimensions.