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.
Highlights
It sometimes happens that systems have multiple discrete vacua or ground states, which is inevitable when a discrete symmetry is spontaneously broken
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 consider the generic case of N ≥ D þ 1 imposing no discrete symmetry and exhaust all exact solutions with full moduli of generic BPS nonplanar networks of domain walls in the infinite Uð1Þ gauge coupling limit in which the model reduces to the CPN−1 model
Summary
It sometimes happens that systems have multiple discrete vacua or ground states, which is inevitable when a discrete symmetry is spontaneously broken. The present authors proposed a model, a D þ 1dimensional Uð1Þ gauge theory [86] admitting novel analytic solutions of the BPS single nonplanar domain wall junctions. We consider the generic case of N ≥ D þ 1 imposing no discrete symmetry and exhaust all exact solutions with full moduli of generic BPS nonplanar networks of domain walls in the infinite Uð1Þ gauge coupling limit in which the model reduces to the CPN−1 model. These are the first exact solutions of nonplanar domain wall networks in D dimensions (D ≥ 3).
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