Abstract
We present a derivation of the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2} that was recently conjectured in Phys. Rev. D 99, 106014 (2019PRVDAQ2470-001010.1103/PhysRevD.99.106014). This is given by the area of an extremal cosmic brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced Rényi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify previously mysterious aspects of negativity at a large central charge seen in conformal blocks and comment on generalizations to generic dimensions, dynamical settings, and quantum corrections.
Highlights
We present a derivation of the holographic dual of logarithmic negativity in AdS3=CFT2 that was recently conjectured in Phys
Introduction.—The von Neumann entropy of the reduced density matrix is an excellent measure of the entanglement between bipartite subsystems in a pure state
It has played a major role in the understanding of how bulk geometry holographically emerges from microscopic degrees of freedom in the anti–de Sitter (AdS)=conformal field theory (CFT) correspondence
Summary
Introduction.—The von Neumann entropy of the reduced density matrix is an excellent measure of the entanglement between bipartite subsystems in a pure state It has played a major role in the understanding of how bulk geometry holographically emerges from microscopic degrees of freedom in the AdS=CFT correspondence. It is an interesting question to ask if and how mixed state entanglement manifests itself geometrically in the bulk in AdS=CFT With motivations from quantum error-correcting codes and preliminary examples in 2D conformal field theory, two of the authors conjectured that logarithmic negativity in holographic conformal field theories is dual to a backreacted entanglement wedge cross section in asymptotically anti–de Sitter (AdS) spacetimes [11], giving a concrete proposal for how mixed state entanglement is geometrized in the bulk.
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