BPS Boojums in N=2 supersymmetric gauge theories II

We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in 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 a gradient flow equations. We analytically/numerically confirm that the negative mass of a single boojum appearing at the end point 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 find a semi-local boojum with a size moduli which appears when the semi-local string ends on the domain wall. We introduce a magnetic scalar potential which offers an intuitive understanding that the end point of vortex string is the source of magnetic field. It can explain that height of the domain wall corresponds to the magnetic scalar potential, but also it gives a physical meaning to the scalar function appearing in the Taubes' equation for BPS Abrikosov-Nilsen-Olesen vortex. Dyonic solutions are also obtained. When the configuration is extended to the dyonic case, the domain wall becomes an electric capacitor storing electric charges on its skin and the boojum charge density becomes proportional to $\vec E \cdot \vec B$. We also find analytic solutions to the 1/4 BPS equations for specific values of the coupling constants. We study the composite solitons from the view points of the Nambu-Goto and Dirac-Born-Infeld actions, and find the semi-local BIon as the counterpart of the semi-local Boojum.