Boundary-bulk relation in topological orders

Understand

In this paper, we study the relation between an anomaly-free $n+$1D topological order, which are often called $n+$1D topological order in physics literature, and its $n$D gapped boundary phases.

• We argue that the $n+$1D bulk anomaly-free topological order for a given $n$D gapped boundary phase is unique.
• This uniqueness defines the notion of the "bulk" for a given gapped boundary phase.
• In this paper, we show that the $n+$1D "bulk" phase is given by the "center" of the $n$D boundary phase.