Abstract
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. These boundary states do not correspond to diagonal RCFT’s in general. These are illustrated in specific Abelian Chern-Simons theories with appropriate boundary conditions.
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ArXiv ePrint: 1908.07700
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Shen, C., Lou, J. & Hung, LY. Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part II. Cutting through the boundary. J. High Energ. Phys. 2019, 168 (2019). https://doi.org/10.1007/JHEP11(2019)168
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DOI: https://doi.org/10.1007/JHEP11(2019)168