The static potential in QED$_3$ with non-minimal coupling

TL;DR

This paper investigates how non-minimal couplings affect the static potential in multiflavor QED3, revealing effects like finite-range repulsion and modifications to photon mass depending on fermion components and coupling strength.

Contribution

It provides a detailed analysis of the impact of non-minimal couplings on the static potential in QED3, including the emergence of finite-range forces and photon mass modifications.

Findings

Non-minimal couplings induce finite-range repulsive forces between opposite charges.

In the four-component case, the photon remains massless and the potential is confining.

In the two-component case, a Chern-Simons term gives the photon a mass, leading to screening.

Abstract

Here we study the effect of the non-minimal coupling $j^{\mu}\eps \partial^{\nu} A^{\alpha} $ on the static potential in multiflavor QED$_3$. Both cases of four and two components fermions are studied separately at leading order in the $1/N $ expansion. Although a non-local Chern-Simons term appears, in the four components case the photon is still massless leading to a confining logarithmic potential similar to the classical one. In the two components case, as expected, the parity breaking fermion mass term generates a traditional Chern-Simons term which makes the photon massive and we have a screening potential which vanishes at large inter-charge distance. The extra non-minimal couplings have no important influence on the static potential at large inter-charge distances. However, interesting effects show up at finite distances. In particular, for strong enough non-minimal coupling we may have a new massive pole in the photon propagator while in the opposite limit there may be no poles at all in the irreducible case. We also found that, in general, the non-minimal couplings lead to a finite range {\bf repulsive} force between charges of opposite signs.