Quantum corrections to holographic entanglement entropy

113

226

Abstract:We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n = 1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the 'operator product expansion' of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n → 1.

Section: Jhep10(2014)178mentioning

confidence: 98%

Twist operators in higher dimensions

Hung

Myers

Smolkin

2014

113

226

“…16 In the figure, the intersection of the entanglement wedge with a bulk Cauchy surface 16 One argument that this must be the case is as follows: the extension by [37] of the Ryu-Takayanagi proposal [38] to next to leading order in 1/N claims that bulk entanglement entropy in the entanglement wedge contributes to the Von Neumann entropy SA. So for example if we have a spin sitting in the entanglement wedge of A that is entangled with another spin in WC [A], then the spin in the entanglement JHEP04 (2015)163 is shaded blue; the minimal area condition causes a discontinuous change as we increase the size of A.…”

Section: Disconnected Regions and Quantum Secret Sharingmentioning

confidence: 99%

Bulk locality and quantum error correction in AdS/CFT

Almheiri

Dong

Harlow

2015

687

1,132

We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

“…Susskind and Uglum proposed that entanglement entropy should renormalize in the same way as (4G N ) −1 [17]. The subject was revisited several times in the past [18][19][20][21][22][23][24][25].…”

Section: Jhep03(2016)033mentioning

confidence: 99%

Holographic RG flows, entanglement entropy and the sum rule

Casini

Testé

Torroba

2016

Abstract:We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.