The Hubeny-Rangamani causal holographic information (CHI) defined by a region $R$ of a holographic quantum field theory (QFT) is a modern version of the idea that the area of event horizons might be related to an entropy. Here the event horizon lives in a dual gravitational bulk theory with Newton's constant $G_{\rm bulk}$, and the relation involves a factor of $4G_{\rm bulk}$. The fact that CHI is bounded below by the von Neumann entropy $S$ suggests that CHI is coarse-grained. Its properties could thus differ markedly from those of $S$. In particular, recent results imply that when $d\le 4$ holographic QFTs are perturbatively coupled to $d$-dimensional gravity, the combined system satisfies the so-called quantum focusing condition (QFC) at leading order in the new gravitational coupling $G_d$ when the QFT entropy is taken to be that of von Neumann. However, by studying states dual to spherical bulk (anti--de Sitter) Schwarschild black holes in the conformal frame for which the boundary is a $(2+1)$-dimensional de Sitter space, we find the QFC defined by CHI is violated even when perturbing about a Killing horizon and using a single null congruence. Since it is known that a generalized second law (GSL) holds in this context, our work demonstrates that the QFC is not required in order for an entropy, or an entropy-like quantity, to satisfy such a GSL.
A Review of the Holographic Relation between Linearized Gravity and the First Law of Entanglement Entropy
本文回顾了Mark van Raamsdonk及其合作者提出的纠缠与引力之间的全息关系。从d维CFT中的纠缠熵第一定律出发，推导出d+1维AdS背景下的线性化Einstein方程，包括有物质和无物质两种情况.这种推导建立在Ryu-Takayanagi公式的基础上，该公式将CFT子系统的纠缠熵与AdS体中的极值表面联系起来。利用Bekenstein-Hawking公式对热场双态和最大扩展AdS/Schwarzschild黑洞之间的对偶性进行了定性研究，证实了引力和纠缠之间的关系.此外，这个定性的论点推广到一般的CFT状态与经典的时空对偶使用Ryu-Takayanagi。论文还回顾了引力和纠缠之间全息关系的最相关的先决条件：Anti-de Sitter时空，纠缠和纠缠熵，规范/引力对偶，Ryu-Takayanagi公式和线性化引力。
We study the dS/CFT duality between minimal type-A higher-spin gravity and the free Sp(2N) vector model. We consider the bulk spacetime as "elliptic" de Sitter space dS_4/Z_2, in which antipodal points have been identified. We apply a technique from arXiv:1509.05890, which extracts the quantum-mechanical commutators (or Poisson brackets) of the linearized bulk theory in an *observable patch* of dS_4/Z_2 directly from the boundary 2-point function. Thus, we construct the Lorentzian commutators of the linearized bulk theory from the Euclidean CFT. In the present paper, we execute this technique …
We consider type-A higher-spin gravity in AdS_4, holographically dual to a free U(N) vector model on the boundary. We study the linearized version of the Didenko-Vasiliev "BPS black hole", which we view as this theory's equivalent of the fundamental string. The Didenko-Vasiliev solution consists of gauge fields of all spins generated by a particle-like source along a bulk geodesic, and is holographically dual to a bilocal boundary operator at the geodesic's endpoints. Our first main result is a new gauge for this solution, which makes manifest its behavior under the boundary field equation. It…
We use the causal horizon entropy to study the asymptotic behaviors of regular AdS black holes. In some literature, the causal horizon entropy is regarded as a generalized holographic $c$-function. In this paper, we apply this idea to the case of regular AdS black holes. We show that the causal horizon entropy decreases to zero at the center of regular AdS black holes and in particular it is stationary because its derivative with respect to the affine parameter approaches zero asymptotically. Meanwhile, the asymptotic behavior of the metric of regular AdS black holes implies that the black hol…
Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity
School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理与天文学院）；Institute of Fundamental Physics and Quantum Technology & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所及物理科学与技术学院）
Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems
Università degli Studi di Pavia（帕维亚大学）；INFN & INDAM, Sezione di Pavia（意大利国家核物理研究所与数学、动力学和应用数学研究所帕维亚分部）；Universität Regensburg（雷根斯堡大学）；McGill University（麦吉尔大学）；City University of Hong Kong（香港城市大学）
Necessary conditions for causality from linearized stability at ultra-high boosts
Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳加尔分校）；National Institute of Science Education and Research（国家科学教育与研究中心）；West University of Timisoara（蒂米什瓦拉西大学）
We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.
We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a …
In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an {\em asymptotic} causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, ${\cal I}^{\pm}$. We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary ``subregions'', (b) is a plausible …
The continuous min flow-max cut principle is used to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- divergenceless norm-bounded timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. The nesting property is used to show the rate of complexity is bounded below by "conditional complexity", describing a multi-step optimization with intermediate and final target states. Conceptually, discretized Lorentzian flows are interpreted in terms of threads or gatelines such that complexity is equal…
We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant descriptio…
