Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories.

@article{Dong2016ShapeDO,
  title={Shape Dependence of Holographic R{\'e}nyi Entropy in Conformal Field Theories.},
  author={Xi Dong},
  journal={Physical review letters},
  year={2016},
  volume={116 25},
  pages={
          251602
        }
}
  • Xi Dong
  • Published 26 February 2016
  • Physics, Medicine
  • Physical review letters
We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy S_{n} is described by two coefficients: f_{b}(n) for traceless extrinsic curvature deformations and f_{c}(n) for Weyl tensor deformations. We provide the first calculation of the coefficient f_{b}(n) in interacting theories by… 

Figures and Topics from this paper

Shape dependence of holographic Rényi entropy in general dimensions
A bstractWe present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our
Universality in the shape dependence of holographic Rényi entropy for general higher derivative gravity
A bstractWe consider higher derivative gravity and obtain universal relations for the shape coefficients (fa, fb, fc) of the shape dependent universal part of the Rényi entropy for four dimensional
Rényi entropy and conformal defects
A bstractWe propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding
The holographic shape of entanglement and Einstein’s equations
A bstractWe study shape-deformations of the entanglement entropy and the modular Hamiltonian for an arbitrary subregion and state (with a smooth dual geometry) in a holographic conformal field
Generalizing the entanglement entropy of singular regions in conformal field theories
Abstract We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for (3 + 1)-dimensional free conformal field
The gravity dual of Rényi entropy
  • Xi Dong
  • Physics, Medicine
    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.
Discrete gravity on random tensor network and holographic Rényi entropy
A bstractIn this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body
Supersymmetric Dualities and Quantum Entanglement in Conformal Field Theory
Conformal field theory (CFT) has been under intensive study for many years. The scale invariance, which arises at the fixed points of renormalization group in relativistic quantum field theory (QFT),
New proposal for a holographic boundary conformal field theory
We propose a new holographic dual of conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our proposal can apply to general boundaries and
Gravity duals of boundary cones
A bstractThe replica trick defines Rényi entropies as partition functions on conically singular geometries. We discuss their gravity duals: regular bulk solutions to the Einstein equations inducing
...
1
2
3
4
...

References

SHOWING 1-10 OF 73 REFERENCES
Entanglement Rényi entropies in conformal field theories and holography
A bstractAn entanglement Rényi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of
Rényi entropy and conformal defects
A bstractWe propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding
Universality in the geometric dependence of Rényi entropy
A bstractWe derive several new results for Rényi entropy, Sn, across generic entangling surfaces. We establish a perturbative expansion of the Rényi entropy, valid in generic quantum field theories,
An Area-Law Prescription for Holographic Renyi Entropies
We show that Renyi entropies satisfy an area law in quantum field theories with a holographic dual description in terms of a bulk gravitational theory. A derivative of the Renyi entropy $S_n$ with
Gravitation from entanglement in holographic CFTs
A bstractEntanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an
Universal entanglement for higher dimensional cones
A bstractThe entanglement entropy of a generic d-dimensional conformal field theory receives a regulator independent contribution when the entangling surface contains a (hyper)conical singularity of
Holographic entanglement entropy for general higher derivative gravity
A bstractWe propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula
Some results on the shape dependence of entanglement and Rényi entropies
We study how the universal contribution to entanglement entropy in a conformal field theory depends on the entangling region. We show that for a deformed sphere the variation of the universal
Anti-de Sitter space and holography
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of
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
...
1
2
3
4
5
...