Domain Walls from $\Sigma(36 \times 3)$, $\Delta(54)$ and $\Delta(27)$ potentials

TL;DR

This paper classifies and calculates the tensions of domain walls arising from scalar potentials invariant under specific discrete symmetry groups, enhancing understanding of topological defects in these models.

Contribution

It provides a systematic classification of domain walls and computes their tensions for potentials with $ ext{Sigma}(36 imes 3)$, $ ext{Delta}(54)$, and $ ext{Delta}(27)$ symmetries, including CP considerations.

Findings

Classified distinct domain walls between degenerate minima.

Calculated the tensions of these domain walls.

Analyzed the impact of CP symmetry on the domain wall structure.

Abstract

We consider the degenerate minima arising from scalar potentials invariant under $\Sigma(36\times 3)$, or under its subgroups $\Delta(54)$ and $\Delta(27)$ (with or without imposed CP symmetries), for a triplet of those symmetries. In this framework, we classify the distinct Domain Walls between the degenerate minima and calculate the respective tensions.