Derivation of Holographic Negativity in AdS_{3}/CFT_{2}.

@article{Kusuki2019DerivationOH,
  title={Derivation of Holographic Negativity in AdS\_\{3\}/CFT\_\{2\}.},
  author={Yuya Kusuki and Jonah Kudler-Flam and Shinsei Ryu},
  journal={Physical review letters},
  year={2019},
  volume={123 13},
  pages={
          131603
        }
}
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… 

Figures from this paper

Entanglement Negativity in Flat Holography
We advance holographic constructions for the entanglement negativity of bipartite states in a class of (1+1)-dimensional Galilean conformal field theories dual to asymptotically flat three
Covariant holographic negativity from the entanglement wedge in AdS$_3/$CFT$_2$
We advance a covariant holographic construction based on the minimal entanglement wedge cross section, for the entanglement negativity of bipartite states in CFT1+1s dual to non static bulk AdS3
Defect extremal surfaces for entanglement negativity
TLDR
In the time-dependent AdS 3 /BCFT 2 scenarios involving eternal black holes in the lower dimensional effective description, the time evolution of the entanglement negativity through the DES and the island formulae is investigated and the analogues of the Page curves are obtained.
Reflected Entropy in AdS$_3$/WCFT
TLDR
It is shown that the reflected entropy can be related holographically to the pre-entanglement wedge cross-section, which is given by the minimal distance between the benches in two swing surfaces.
Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
We investigate the application of a holographic entanglement negativity construction to bipartite states of single subsystems in CFTds with a conserved charge dual to bulk AdSd+1 geometries. In this
Holographic Entanglement Negativity for Disjoint Subsystems in Conformal Field Theories with a Conserved Charge
We investigate the extension of a holographic construction for the entanglement negativity of two disjoint subsystems in proximity to CFTds with a conserved charge dual to bulk AdSd+1 geometries. The
Reflected entropy in Galilean conformal field theories and flat holography
We obtain the reflected entropy for bipartite states in a class of (1 + 1)-dimensional Galilean conformal field theories (GCFT1+1) through a replica technique. Furthermore we compare our results with
On minimal entanglement wedge cross section for holographic entanglement negativity
We propose an alternate construction to compute the minimal entanglement wedge cross section (EWCS) for a single interval in a $(1+1)$ dimensional holographic conformal field theory at a finite
Holographic entanglement negativity for disjoint subsystems in $\mathrm{AdS_{d+1}/CFT_d}$
We propose a construction to compute the holographic entanglement negativity for bipartite mixed state configurations of two disjoint subsystems (in proximity) in higher dimensional conformal field
Entanglement wedge in flat holography and entanglement negativity
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space
...
...

References

SHOWING 1-10 OF 59 REFERENCES
Holographic Derivation of Entanglement Entropy from AdS/CFT
A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal
Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.
TLDR
It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.
Aspects of Holographic Entanglement Entropy
This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a
Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the
Entanglement negativity in extended systems: A field theoretical approach
We report on a systematic approach for the calculation of the negativity in the ground state of a one-dimensional quantum field theory. The partial transpose rho_A^{T_2} of the reduced density matrix
Entanglement of purification through holographic duality
The gauge/gravity correspondence discovered two decades ago has had a profound influence on how the basic laws in physics should be formulated. In spite of the predictive power of holographic
Finite temperature entanglement negativity in conformal field theory
We consider the logarithmic negativity of a finite interval embedded in an infinite one dimensional system at finite temperature. We focus on conformal invariant systems and we show that the naive
Entanglement negativity in quantum field theory.
TLDR
A systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory is developed, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem and applied to conformal field theories.
The gravity dual of Rényi entropy
  • Xi Dong
  • Physics, Computer Science
    Nature communications
  • 2016
TLDR
It is shown that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes, a one-parameter generalization of the minimal surface prescription for entanglement entropy.
A covariant holographic entanglement entropy proposal
With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal
...
...