Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers

Understand

In this paper, we study the relation between topological orders and their gapped boundaries.

• We propose that the bulk for a given gapped boundary theory is unique.
• It is actually a consequence of a microscopic definition of a local topological order, which is a (potentially anomalous) topological order defined on an open disk.
• Using this uniqueness, we show that the notion of "bulk" is equivalent to the notion of center in mathematics.