Domain Walls and Double Bubbles

TL;DR

This paper explores how intersecting domain walls in a specific field theory can model double bubble configurations, providing a new approach to understanding minimal surface structures in different topologies.

Contribution

It introduces a volume-preserving flow in a Wess-Zumino model to realize double bubble configurations as static solutions, linking field theory to minimal surface problems.

Findings

Constructed phase diagrams for double bubbles in 2D tori

Reconstructed known double bubble examples in 3D tori

Demonstrated the field theory approach models minimal surfaces

Abstract

We study configurations of intersecting domain walls in a Wess-Zumino model with three vacua. We introduce a volume-preserving flow and show that its static solutions are configurations of intersecting domain walls that form double bubbles, that is, minimal area surfaces which enclose and separate two prescribed volumes. To illustrate this field theory approach to double bubbles, we use domain walls to reconstruct the phase diagram for double bubbles in the flat square two-torus and also construct all known examples of double bubbles in the flat cubic three-torus.