Derivation of holographic negativity in AdS${}_3$/CFT${}_2$

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 (2019)]. 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 large central charge seen in conformal blocks and comment on generalizations to generic dimensions, dynamical settings, and quantum corrections.

4+2 pages. v2: supplemental material fixed and references added to match published version in PRL. v3: assumption regarding OPE coefficient clarified

References in corpus (5)

• Entanglement negativity in quantum field theory
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Finite temperature entanglement negativity in conformal field theory
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Conformal Blocks and Negativity at Large Central Charge

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