Vortices and Monopoles in a Harmonic Trap

TL;DR

This paper investigates the behavior and dynamics of BPS monopoles and vortices confined in a harmonic trap, revealing their rich collective coordinate structure and how it evolves with trap strength.

Contribution

It provides a detailed analysis of confined monopoles in a harmonic trap, including an index theorem for their collective coordinates and insights into their dynamic behavior.

Findings

Confined monopoles have quadratic mass in topological charges.

Number of collective coordinates varies with trap strength.

Monopoles can disappear or emerge as the trap strength changes.

Abstract

The Omega-deformation is a harmonic trap, penning certain excitations near the origin in a manner consistent with supersymmetry. Here we explore the dynamics of BPS monopoles and vortices in such a trap. We pay particular attention to monopoles in the Higgs phase, when they are confined to a vortex string. Unusually for BPS solitons, the mass of these confined monopoles is quadratic in the topological charges. We compute an index theorem to determine the number of collective coordinates of confined monopoles. Despite being restricted to move on a line, we find that they have a rich dynamics. As the strength of the trap increases, the number of collective coordinates can change, sometimes with constituent monopoles disappearing, sometimes with new ones emerging.