BPS Boojums in N=2 supersymmetric gauge theories I

TL;DR

This paper investigates 1/4 BPS composite solitons in N=2 supersymmetric Abelian gauge theories, providing analytical and numerical solutions, and clarifying the properties and dependencies of boojums, vortex strings, and domain walls.

Contribution

It offers new analytical and numerical solutions to 1/4 BPS equations, including approximate functions for generic couplings and insights into boojum properties.

Findings

Confirmed the negative mass of a boojum equals half the monopole mass.

Developed globally correct approximate functions for numerical solutions.

Clarified how boojum shape depends on coupling constants and moduli.

Abstract

We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in ${\cal N}=2$ supersymmetric Abelian gauge theories in four dimensions. We obtain solutions to the 1/4 BPS equations with the finite gauge coupling constant. To obtain numerical solutions for generic coupling constants, we construct globally correct approximate functions which allow us to easily find fixed points of gradient flow equations. We analytically/numerically confirm that the negative mass of a single boojum appearingat the endpoint of the vortex string on the logarithmically bent domain wall is equal to the half-mass of the 't Hooft-Polyakov monopole. We examine various configurations and clarify how the shape of the boojum depends on the coupling constants and moduli parameters. We also find analytic solutions to the 1/4 BPS equations for specific values of the coupling constants.