Collapsing domain walls beyond Z2

Discrete symmetries are widely imposed in particle theories. It is well known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of a ${Z}_{2}$ symmetry. Larger discrete symmetries have multiple degenerate vacua, leading to domain walls which are in principle different from the simplest ${Z}_{2}$ domain wall. We take domain walls from ${Z}_{N}$ symmetry breaking as an illustrative study, and study in detail the ${Z}_{3}$ case, in which semianalytical results for the tension and thickness of domain walls are derived. Explicit symmetry-breaking terms lead to the dynamics of domain walls collapsing in a more more complicated way than the ${Z}_{2}$ case. Gravitational wave signals deviate from those from ${Z}_{2}$ domain walls.