Winding number dependence of quantum vortex energies at one-loop

TL;DR

This paper calculates quantum corrections to vortex energies in scalar electrodynamics, revealing that vacuum polarization energies depend on winding number and influence vortex stability.

Contribution

It provides the first detailed one-loop vacuum polarization energy calculation for ANO vortices with arbitrary winding number in the BPS case.

Findings

Vacuum polarization energy is negative and roughly proportional to winding number minus one.

Quantum corrections modify the classical energy dependence on winding number.

Results inform stability analysis of higher winding vortices.

Abstract

We compute the one-loop vacuum polarization energies of Abrikosov-Nielsen-Olesen (ANO) vortices with topological charge $n$ in scalar electrodynamics, for the BPS case of equal gauge and scalar masses. This calculation allows us to investigate the relationship between the winding number and the quantum-corrected vortex energy, which in turn determines the stability of higher winding configurations against decay into configurations with unit winding. While the classical energy is proportional to $n$, we find that the vacuum polarization energy is negative and approximately proportional to $n-1$ with a small constant offset.