A note on entanglement entropy and regularization in holographic interface theories

Abstract

We discuss the computation of holographic entanglement entropy for interface conformal field theories. The fact that globally well defined Fefferman-Graham coordinates are difficult to construct makes the regularization of the holographic theory challenging. We introduce a simple new cut-off procedure, which we call "double cut-off" regularization. We test the new cut-off procedure by comparing the results for holographic entanglement entropies using other cut-off procedures and find agreement. We also study three dimensional conformal field theories with a two dimensional interface. In that case the dual bulk geometry is constructed using warped geometry with an $Ad{S}_3$ factor. We define an effective central charge to the interface through the Brown-Henneaux formula for the $Ad{S}_3$ factor. We investigate two concrete examples, showing that the same effective central charge appears in the computation of entanglement entropy and governs the conformal anomaly.

38 pages

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• Holographic Complexity for Defects Distinguishes Action from Volume
• Energy Reflection and Transmission at 2D Holographic Interfaces
• Janus solutions in six-dimensional gauged supergravity
• Phases of Holographic Interfaces
• Energy Transport for Thick Holographic Branes
• Entanglement Phase Transition in Holographic Pseudo Entropy
• Holographic line defects in F(4) gauged supergravity
• Holographic Computations of the Quantum Information Metric
• Entanglement evolution across a conformal interface
• Volume complexity for Janus ${\mathrm{AdS}}_3$ geometries
• Action complexity in the presence of defects and boundaries
• Transport across interfaces in symmetric orbifolds
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• Quantum Information Metric on $\mathbb{R}\times S^{d-1}$
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories