Remarks on the static potential driven by vacuum nonlinearities in $D=3$ models

TL;DR

This paper investigates how vacuum nonlinearities in three-dimensional models affect static potentials, revealing long-range corrections and confinement phenomena through analysis of generalized Born-Infeld, Pagels-Tomboulis-like, and Euler-Heisenberg-like electrodynamics.

Contribution

It demonstrates the equivalence of generalized Born-Infeld and Pagels-Tomboulis-like models and uncovers confinement effects in Euler-Heisenberg-like electrodynamics.

Findings

Generalized Born-Infeld and Pagels-Tomboulis-like models are equivalent.

Long-range 1/r^2 correction to Coulomb potential in certain models.

Linear potential indicating charge confinement in Euler-Heisenberg-like model.

Abstract

Within the framework of the gauge-invariant, but path-dependent, variables formalism, we study the manifestations of vacuum electromagnetic nonlinearities in $D=3$ models. For this we consider both generalized Born-Infeld and Pagels-Tomboulis-like electrodynamics, as well as, an Euler-Heisenberg-like electrodynamics. We explicitly show that generalized Born-Infeld and Pagels-Tomboulis-like electrodynamics are equivalent, where the static potential profile contains a long-range (${\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle {{r^2}}$}}$-type) correction to the Coulomb potential. Interestingly enough, for an Euler-Heisenberg-like electrodynamics the interaction energy contains a linear potential, leading to the confinement of static charges.