Dynamics of domain wall networks

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli approximation and find a phase rotation induces a repulsive force which can be understood as a Noether charge of Q-solitons. Non-Abelian gauge theory allows different types of loops which can be deformed to each other by changing a modulus. This admits the moduli geometry like a sandglass made by gluing the tips of the two cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes of all loops tend to grow for a late time in general models with complex Higgs masses, while the sizes are stabilized at some values once triplet masses are introduced for the Higgs fields. We also show that the stationary motion on the moduli space of the domain wall webs represents 1/4 Bogomol'nyi-Prasad- Sommerfield Q-webs of walls.