Tiling the plane without supersymmetry

TL;DR

This paper introduces a stable, supersymmetry-free method for tiling the plane using a hexagonal defect network derived from a two-scalar field model with $Z_3$ symmetry, applicable in both vacuum and defect sectors.

Contribution

It demonstrates a novel construction of a stable hexagonal defect network without relying on supersymmetry, based on a $Z_3$ symmetric two-scalar field model.

Findings

The network is stable due to three-junctions in the model.

The $Z_3$ symmetry governs both vacuum and defect sectors.

No supersymmetry is necessary for the network's stability.

Abstract

We present a way of tiling the plane with a regular hexagonal network of defects. The network is stable and follows in consequence of the three-junctions that appear in a model of two real scalar fields that presents $Z_3$ symmetry. The $Z_3$ symmetry is effective in both the vacuum and defect sectors, and no supersymmetry is required to build the network.