BPS boojums in ${\cal N}=2$ supersymmetric gauge theories I

Abstract

We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in 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 appearing at 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.

Non-Abelian gauge field localization on walls and geometric Higgs mechanism

“…Lastly, many similarities between domain walls and D-branes have been shown in the literature. For example, D1-D3-like configuration was found in [27][28][29][30][31][32][33][34][35][36]. Furthermore, the low-energy effective theory on domain walls was found to be similar to that on D-branes [37][38][39]46].…”

Vacua and walls of mass-deformed Kähler nonlinear sigma models on SO(2N)/U(N)

“…Domain walls and domain wall webs are discussed in [5,6,7]. Other BPS objects and composite objects are discussed in [8,9,10,11,12,13,14].…”

BPS boojums in ${\cal N}=2$ supersymmetric gauge theories II

“…However, it is not straightforward task to give it when two or more topological solitons coexist. In [17], we provided a simple and systematic way to give suitable boundary conditions called the global approximations. We showed that the global approximation is useful not only to solve numerically the master equation but also to figure out the boojum mass exactly without any ambiguity, such as that discussed in [16].…”

“…In our previous work [17], we were oriented to solving the master equation and revealing real shape of the boojums. In contrast, in this paper we will focus on physical aspects of the boojums and expand our understanding of composite solitons further by using the developments of our previous work [17]. First we investigate a composite solution that a (semi-)local string vortex ends on a wall in a weak gauge coupling limit.…”

“…Section 2 serves as a summary of our model and all relevant formulas, such as topological charges and 1/4 BPS equations, which we present both in terms of field and also via moduli matrix method. In that section, we do not repeat derivation of these quantities, which is done in [17]. In Section 3 we present the notion of a boojum as a fractional magnetic monopole.…”