Classification of Abelian domain walls

We discuss domain walls from spontaneous breaking of Abelian discrete symmetries $Z_N$. A series different wall structures are predicted, depending on the symmetry and charge assignments scalars leading to (SSB). widely-existing type those separating degenerate vacua which adjacent in field space. denote these as adjacency walls. In case that $Z_N$ terms small compared with $U(1)$ terms, SSB generates strings first then bounded by generated after For larger than $Z_3$, non-adjacent exist, we regard them non-adjacency These unstable if is a good approximation. If broken via multiple steps, arrive at complex structure one kind wrapped another type. On other hand, directions independently, chains blind each other.