Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions

TL;DR

This paper calculates the energies and energy densities of static electromagnetic flux tubes in 2+1 and 3+1 dimensions using exact one-loop scattering data, revealing similarities across dimensions and validating approximation methods.

Contribution

It provides an exact one-loop calculation of flux tube energies in different dimensions, clarifying previous discrepancies and comparing with approximation techniques.

Findings

Energy dependence on flux tube parameters is similar in 2+1 and 3+1 dimensions.

Good agreement between exact results and approximation methods for certain parameters.

Remedies previous puzzles in the literature regarding flux tube energies.

Abstract

We compute energies and energy densities of static electromagnetic flux tubes in three and four spacetime dimensions. Our calculation uses scattering data from the potential induced by the flux tube and imposes standard perturbative renormalization conditions. The calculation is exact to one-loop order, with no additional approximation adopted. We embed the flux tube in a configuration with zero total flux so that we can fully apply standard results from scattering theory. We find that upon choosing the same on-shell renormalization conditions, the functional dependence of the energy and energy density on the parameters of the flux tube is very similar for three and four spacetime dimensions. We compare our exact results to those obtained from the derivative and perturbation expansion approximations, and find good agreement for appropriate parameters of the flux tube. This remedies some puzzles in the prior literature.