Entanglement and topological interfaces

Abstract

In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.

30 pages, 2 figures. References added, typos corrected

References in corpus (6)

• Duality and defects in rational conformal field theory
• Fusion of conformal interfaces
• Entanglement through conformal interfaces
• Solution of the fermionic entanglement problem with interface defects
• Left-Right Entanglement Entropy of Boundary States
• Supersymmetric Renyi Entropy in $CF{T}_2$ and $Ad{S}_3$

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• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Rényi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions
• Multipartite entanglement in two-dimensional chiral topological liquids
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
• Defects and Perturbation
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• LREE of a Dressed D$p$-brane with Transverse Motion in the Partially Compact Spacetime