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

## TL;DR

This paper derives the holographic dual of logarithmic negativity in AdS3/CFT2, relating it to extremal cosmic branes and clarifying its behavior at large central charge, with implications for broader holographic settings.

## Contribution

It provides a rigorous derivation of the holographic negativity formula using Rènyi reflected entropy and explores its properties and generalizations.

## Key findings

- Holographic negativity corresponds to extremal cosmic brane area.
- Clarification of negativity behavior at large central charge.
- Discussion of extensions to other dimensions and dynamical scenarios.

## 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 R\'enyi 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.