Confinement and chiral condensates in 2-d QED with massive N-flavor fermions

TL;DR

This paper investigates the effects of external charges and electric fields on confinement and chiral condensates in two-dimensional QED with multiple fermion flavors, revealing phase shifts and singularities in string tension.

Contribution

It provides a detailed analysis of how external charges influence the vacuum structure, chiral condensates, and string tension in 2D QED with massive N-flavor fermions, including finite temperature effects.

Findings

Shift in vacuum angle $ heta$ is proportional to external charge $q$

String tension exhibits cusp singularity at $ heta= \\pm \\pi$ for $N \\ge 2$

String tension scales as $m^{2N/(N+1)}$ at zero temperature

Abstract

We evaluate Polyakov loops and string tension in two-dimensional QED with both massless and massive $N$-flavor fermions at zero and finite temperature. External charges, or external electric fields, induce phases in fermion masses and shift the value of the vacuum angle parameter $\theta$, which in turn alters the chiral condensate. In particular, in the presence of two sources of opposite charges, $q$ and $-q$, the shift in $\theta$ is $2\pi(q/e)$ independent of $N$. The string tension has a cusp singularity at $\theta=\pm\pi$ for $N\ge 2$ and is proportional to $m^{2N/(N+1)}$ at $T=0$.