Gravity edges modes and Hayward term

Self Cite

We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems.

Section: Discussionmentioning

confidence: 61%

A field theory study of entanglement wedge cross section: odd entropy

Mollabashi

Tamaoka

2020

Self Cite

“…Since the boundary is fixed previously, the corner angle is arbitrarily fixed and the Hayward term is required to get a well posed variational problem. In a very recent article [15] Takayanagi and Tamaoka drew attention to a possible application of this term to holographic context and to the study of the entanglement entropy; in particular, using a replica trick calculation close to the Fursaev's approach [5], they showed that the von Neumann entanglement entropy can be explained by considering the Hayward term in the gravitational action. The aim of the present work is to generalize this result to the Rényi entropies, precisely by showing that the cosmic brane term is explained in the own gravitational theory through a Hayward term.…”

Section: Introductionmentioning

confidence: 99%

Rényi entropies and area operator from gravity with Hayward term

Botta-Cantcheff

Martínez

Zarate

2020

In the context of the holographic duality, the entanglement entropy of ordinary QFT in a subregion in the boundary is given by a quarter of the area of an minimal surface embedded in the bulk spacetime. This rule has been also extended to a suitable one-parameter generalization of the von-Neuman entropyŜ n that is related to the Rényi entropies S n , as given by the area of a cosmic brane minimally coupled with gravity, with a tension related to n that vanishes as n → 1, and moreover, this parameter can be analytically extended to arbitrary real values. However, the brane action plays no role in the duality and cannot be considered a part of the theory of gravity, thus it is used as an auxiliary tool to find the correct background geometry. In this work we study the construction of the gravitational (reduced) density matrix from holographic states, whose wave-functionals are described as euclidean path integrals with arbitrary conditions on the asymptotic boundaries, and argue that in general, a nontrivial Hayward term must be haven into account. So we propose that the gravity model with a coupled Nambu-Goto action is not an artificial tool to account for the Rényi entropies, but it is present in the own gravity action through a Hayward term. As a result we show that the computations using replicas simplify considerably and we recover the holographic prescriptions for the measures of entanglement entropy; in particular, derive an area law for the original Rényi entropies (S n) related to a minimal surface in the n replicated spacetime. Moreover, we show that the gravitational modular flow contains the area operator and can explain the Jafferis-Lewkowycz-Maldacena-Suh proposal.

“…While it did not seem to play an important role in our discussion, a Hayward term might need to be included [45] (for recent work, see e.g. [46]). A thorough analysis could lead to an extended holographic dictionary between bulk modes and fields localized on the brane.…”

Section: Discussionmentioning

confidence: 99%

Brane dynamics from the first law of entanglement

Cooper

Neuenfeld

Rozali

et al. 2020

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the BCFT, and using Wald's covariant phase space formalism in the presence of boundaries, we derive constraints from the first law for a broad range of covariant bulk Lagrangians. We explicitly evaluate these constraints for Einstein gravity, and find a local equation on the brane which is precisely the Neumann condition of Takayanagi [arXiv:1105.5165] at linear order in metric perturbations. This is analogous to the derivation of Einstein's equations from the first law of entanglement entropy. This machinery should generalize to give local linearized equations of motion for higher-derivative bulk gravity with additional fields. arXiv:1912.05746v1 [hep-th]