Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary

Understand

We compute the entanglement entropy in a 2+1 dimensional topological order in the presence of gapped boundaries.

• Specifically, we consider entanglement cuts that cut through the boundaries.
• We argue that based on general considerations of the bulk-boundary correspondence, the "twisted characters" feature in the Renyi entropy, and the topological entanglement entropy is controlled by a "half-linking number" in direct analogy to the role played by the S-modular matrix in the absence of boundaries.
• We also construct a class of boundary states based on the half-linking numbers that provides a "closed-string" picture complementing an "open-string" computation of the entanglement entropy.