Quantum energies of BPS vortices in $D=2+1$ and $D=3+1$

TL;DR

This paper calculates the leading quantum corrections to BPS vortex energies in scalar electrodynamics for 2+1 and 3+1 dimensions, revealing negative, linearly scaling corrections that favor combined vortices.

Contribution

It provides the first detailed analysis of quantum energy corrections for BPS vortices in both 2+1 and 3+1 dimensions, focusing on the dependence on winding number.

Findings

Quantum corrections are negative for both dimensions.

Corrections scale approximately linearly with winding number n.

Combined vortices are energetically favored over isolated ones.

Abstract

We consider vortices in scalar electrodynamics and compute the leading quantum correction to their energies for the BPS case of identical classical masses of the Higgs and gauge fields. In particular, we focus on the winding number $n$ dependence of these corrections, from which we can extract the binding energies of configurations with larger $n$. For both dimensionalities, $D=2+1$ and $D=3+1$, we find that quantum corrections are negative and scale approximately linearly with $n$, so that combined vortices are favored over isolated ones.