A remark on gapped domain walls between topological phases

Understand

We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase.

• We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics based on works of Davydov, M\"uger, Nikshych and Ostrik.
• In particular, we identify their tunneling matrix and a coupling matrix of Rehren, and show that their conjecture does not hold.