Confinement in the presence of external fields and axions

TL;DR

This paper investigates how external electric and magnetic fields influence confinement phenomena in gauge theories with pseudoscalar couplings, revealing Coulombic behavior in electric fields and confining potentials in magnetic fields.

Contribution

It provides a detailed calculation of the static potential in the presence of external fields using gauge-invariant variables, highlighting the emergence of confinement under magnetic conditions.

Findings

Electric field expectation preserves Coulomb potential.

Magnetic field expectation leads to Yukawa plus linear confining potential.

External magnetic fields induce confinement of static charges.

Abstract

For a theory with a pseudo scalar coupling $\phi F\tilde F$ and in the case that there is a constant electric or magnetic strength expectation value, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. While in the case of a constant electric field strength expectation value the static potential remains Coulombic, in the case of a constant magnetic field strength the potential energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static charges.