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Journal of High Energy Physics

, 2019:168 | Cite as

Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part II. Cutting through the boundary

  • Ce ShenEmail author
  • Jiaqi Lou
  • Ling-Yan Hung
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Anyons Conformal Field Theory Chern-Simons Theories Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Surface PhysicsFudan UniversityShanghaiChina
  2. 2.Collaborative Innovation Center of Advanced MicrostructuresNanjingChina
  3. 3.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina
  4. 4.Institute for Nanoelectronic Devices and Quantum computingFudan UniversityShanghaiChina

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