Screening vs. Confinement in 1+1 Dimensions

TL;DR

This paper demonstrates that in 1+1 dimensional gauge theories, heavy probe charges are screened by massless fermions, and confinement re-emerges when fermions acquire mass, with implications for higher-dimensional theories.

Contribution

It reveals unexpected screening phenomena in 1+1D gauge theories, including fractional charge screening, and analyzes the transition to confinement as fermion mass increases.

Findings

Heavy probes are screened by massless fermions in 1+1D.

Screening disappears and confinement is restored with non-zero fermion mass.

String tension at small mass is proportional to fermion mass and condensate.

Abstract

We show that, in 1+1 dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in $QCD_2$ with adjoint massless Majorana fermions. The screening disappears and confinement is restored as soon as the dynamical fermions are given a non-zero mass. For small masses, the string tension is given by the product of the light fermion mass and the fermion condensate with a known numerical coefficient. Parallels with 3+1 dimensional $QCD$ and supersymmetric gauge theories are discussed.