BPS Boojums in N=2 supersymmetric gauge theories I

Abstract

We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in $\mathcal{N}=2$ 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.

69 pages, 27 figures. Ver. 1 has been divided into two papers and this paper is the first part of the division. The second part will soon appear with the title "BPS Boojums in N=2 supersymmetric gauge theories II"

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Cited by in corpus (4)

• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $SO(2N)/U(N)$
• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $Sp(N)/U(N)$
• Non-Abelian Gauge Field Localization on Walls and Geometric Higgs Mechanism
• Exact BPS domain walls at finite gauge coupling