Real and Imaginary Mass Generation in the Presence of External Fields and Axions

TL;DR

This paper investigates how external electric and magnetic fields influence mass generation and vacuum energy in a pseudo scalar field theory, revealing magnetic mass generation and electric tachyonic instability at high field strengths.

Contribution

It demonstrates the distinct effects of electric and magnetic fields on mass generation and vacuum energy in pseudo scalar field theories, including exact vacuum energy evaluation.

Findings

Magnetic fields induce mass for perturbations.

Electric fields cause tachyonic mass at high strength.

Vacuum energy acquires an imaginary part beyond critical electric field.

Abstract

Small fluctuations around a constant electric or constant magnetic field F are analyzed in a theory with pseudo scalar [phi] with a coupling g[phi]F~F. It is found that a magnetic external field leads to mass generation for the small perturbations, while an electric field suffers from a tachyonic mass generation in the case in which the field strength is higher than a critical value (related to the pseudo scalar mass). The vacuum energy can be exactly evaluated and it is found that an imaginary part is present when the external electric field exceeds its critical value.