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

Yuya Kusuki, Jonah Kudler-Flam, Shinsei Ryu

TL;DR

The derivation of the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2} that was recently conjectured is presented and previously mysterious aspects of negativity at a large central charge seen in conformal blocks are clarified.

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.

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

TL;DR

The derivation of the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2} that was recently conjectured is presented and previously mysterious aspects of negativity at a large central charge seen in conformal blocks are clarified.

Abstract

We present a derivation of the holographic dual of logarithmic negativity in AdS/CFT 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.

Paper Structure

This paper contains 1 section, 43 equations, 1 figure.

Table of Contents

  1. Supplemental Material

Figures (1)

  • Figure 1: The blue line is the negativity that comes from the Virasoro block computed to order $q^{500}$ using Zamolodchikov's recursion relation where $q$ is the elliptic nome. The yellow line shows the minimal entanglement wedge cross section (\ref{['ew_disjoing']}). Here we set $c=10$ and ${\epsilon}=10^{-2}$, and in this plot, we divide these quantities by $c$ to rescale.