Computing data for Levin-Wen with defects

TL;DR

This work demonstrates how to do many computations for doubled topological phases with defects using generalized tube algebra techniques, and shows all possible point defects, and the fusion and associator data of these.

Abstract

We demonstrate how to do many computations for non-chiral topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects. Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate how domain wall fusion and associators can be computed using generalized tube algebra techniques. These domain walls can be both between distinct or identical phases. Additionally, we show how to compute all possible point defects, and the fusion and associator data of these. Worked examples, tabulated data and Mathematica code are provided.