Anomalous Behavior in the Massive Schwinger Model

TL;DR

This paper investigates nonperturbative phenomena in the massive Schwinger model, revealing discontinuous and anomalous behaviors in chiral condensate and Polyakov loop related to vacuum structure at specific parameters.

Contribution

It introduces a detailed analysis of the vacuum eigenvalue solutions, uncovering bifurcation processes causing anomalous behaviors in the model.

Findings

Discontinuous dependence of chiral condensate on fermion mass.

Anomalous temperature dependence of Polyakov loops near $ heta \,\sim\,\pi$.

Bifurcation in vacuum eigenvalue solutions explains nonperturbative phenomena.

Abstract

We evaluate the chiral condensate and Polyakov loop in two-dimensional QED with a fermion of an arbitrary mass ($m$). We find discontinuous $m$ dependence in the chiral condensate and anomalous temperature dependence in Polyakov loops when the vacuum angle $\theta$$\sim$$\pi$ and $m$=O($e$). These nonperturbative phenomena are due to the bifurcation process in the solutions to the vacuum eigenvalue equation.