Classification of Abelian domain walls

TL;DR

This paper classifies various structures of domain walls resulting from the spontaneous breaking of Abelian discrete symmetries, highlighting their formation, stability, and complex configurations depending on symmetry breaking patterns.

Contribution

It provides a comprehensive classification of Abelian domain wall structures, including adjacency and non-adjacency walls, and analyzes their formation and stability under different symmetry breaking scenarios.

Findings

Adjacency walls separate degenerate vacua in field space.

Non-adjacency walls exist for larger symmetries and are unstable if $U(1)$ is a good approximation.

Complex wall structures arise from multi-step symmetry breaking.

Abstract

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