Domain walls in topological phases and the Brauer-Picard ring for $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$

Understand

We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams.

• As an illustrative example, we compute the Brauer-Picard ring for the fusion category $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$.
• Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase.
• We show how this interpretation can be used to compute the Brauer-Picard ring from a physical perspective.