Degenerate vortices and world-line instantons in three-dimensional gauge theories

TL;DR

This paper investigates quantum mixing and splitting of degenerate vortices in 2+1-dimensional gauge theories, extending previous 1+1-dimensional studies, and explores the role of supersymmetry in protecting BPS vortices.

Contribution

It extends the analysis of topological soliton mixing from 1+1 dimensions to 2+1 dimensions, highlighting quantum effects and supersymmetry protection mechanisms.

Findings

Degenerate vortices generally mix and split quantum mechanically.

Supersymmetry protects BPS vortices only with sufficient supercharges.

Quantum effects differ from classical degeneracy in vortices.

Abstract

In this paper we continue the study of particle-like topological solitons with degenerate masses and their mixing due to world-line instantons. Previously, this phenomenon was studied in 1+1-dimensional setups. Here we take a step further and consider degenerate vortices in 2+1 dimensions. We find that, while classically such vortices may be degenerate, they generally mix and split at the quantum level. Supersymmetry protects BPS-saturated vortices only when the number of supercharges in the bulk is large enough.