Exhausting all exact solutions of BPS domain wall networks in arbitrary dimensions

Abstract

We obtain full moduli parameters for generic non-planar BPS networks of domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields, and exhaust all exact solutions in the corresponding $\mathbb{C}{P}^{N-1}$ model. We develop a convenient description by grid diagrams which are polytopes determined by mass parameters of the model. To illustrate the validity of our method, we work out non-planar domain wall networks for lower $N$ in $3+1$ dimensions. In general, the networks can have compact vacuum bubbles, which are finite vacuum regions surrounded by domain walls, when the polytopes of the grid diagrams have inner vertices, and the size of bubbles can be controlled by moduli parameters. We also construct domain wall networks with bubbles in the shapes of the Platonic, Archimedean, Catalan, and Kepler-Poinsot solids.

35 pages, 15 figures

References in corpus (20)

• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Webs of Walls
• Global Structure of Moduli Space for BPS Walls
• Domain Walls with Non-Abelian Clouds
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• Intersecting Solitons, Amoeba and Tropical Geometry
• Effective Action of Domain Wall Networks
• D-brane Configurations for Domain Walls and Their Webs
• Dynamics of Strings between Walls
• Walls of massive Kähler sigma models on SO(2N)/U(N) and Sp(N)/U(N)
• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $SO(2N)/U(N)$
• Exact solutions of domain wall junctions in arbitrary dimensions
• Junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ II

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