Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction

TL;DR

This paper investigates the holographic duality between reflected entropy and entanglement wedge cross section, incorporating first order corrections, and demonstrates their agreement in a perturbed setting within holographic conformal field theories.

Contribution

It provides the first perturbative analysis of the reflected entropy and entanglement wedge cross section duality with first order corrections in holographic CFTs.

Findings

Perfect agreement between field theory and gravity calculations with first order correction.

Perturbative computation of reflected entropy using semiclassical conformal blocks.

Backreacted geometry analysis confirms the duality with first order correction.

Abstract

We study the holographic duality between the reflected entropy and the entanglement wedge cross section with the first order correction. In the field theory side, we consider the reflected entropy for $\rho_{AB}^m$, where $\rho_{AB}$ is the reduced density matrix for two intervals in the ground state. The reflected entropy in the 2d holographic conformal field theories is computed perturbatively up to the first order in $m-1$ by using the semiclassical conformal block. In the gravity side, we compute the entanglement wedge cross section in the backreacted geometry by cosmic branes with tension $T_m$ which are anchored at the AdS boundary. Comparing both results we find a perfect agreement, showing the duality works with the first order correction in $m-1$.