Chia-Jui Chou, Bo-Han Lin, Bin Wang, Yi Yang
We study entanglement entropy inequalities in boundary conformal field theory (BCFT) by holographic correspondence. By carefully classifying all the configurations for different phases, we prove the strong subadditiviy and the monogamy of mutual information for holographic entanglement entropy in BCFT at both zero and finite temperatures
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We explore some aspects of holographic dual of Boundary Conformal Field Theory (BCFT). In particular we study asymptotic symmetry of geometries which provide holographic dual of BCFTs. We also compute two-point functions of certain bosonic and fermionic operators in the dual BCFT by making use of AdS/BCFT correspondence.
Resolving BCFT bulk-cone singularities in braneworlds and top-down holography
本文研究了全息BCFT中的体锥奇异性，通过在膜世界对偶中引入弦理论修正和冲击波几何来限制两点函数，从而解决该奇异性，并将此方法扩展至D1/D5 BCFT的自上而下全息模型。
Recently, boundary conformal field theories (BCFTs) have attracted much attention in the context of quantum gravity. This is because a BCFT can be dual to gravity coupled to a heat bath CFT, known as the island model. On this background, it would be interesting to explore the duality between the boundary and the braneworld. However, this seems to be a challenging problem. The reason is because although there has been much study of rational BCFTs, there has been comparatively little study of irrational BCFTs, and irrational BCFTs are expected to be the boundary duals of the braneworlds. For thi…
In this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing functions under the RG flows. We present a few supporting evidences from field theory calculations. In two dimensions, we give a holographic construction (AdS/BCFT) for an arbitrary shape of boundary and calculate its logarithmic term as well as boundary energy momentum tensors, confirming its consistency with the Weyl anomaly. Moreover, we give perturbative solut…
Flat Space Holography via AdS/BCFT
本文通过构造EOW膜世界体为平坦空间的AdS/BCFT构型，提出平坦空间引力对偶于卡罗尔CFT，并给出零边界CFT的纠缠熵、关联函数与配分函数的新全息预言。
Holography for BCFTs with Multiple Boundaries: Multi-Splitting Quenches
该研究通过全息方法探讨了具有多个边界的BCFTs的纠缠熵随时间变化，针对N=4和N=17给出了显式结果，并发现较大N的差异在N=4时已显现。
We develop the notion of double holography in Type IIB string theory realizations of braneworld models. The Type IIB setups are based on the holographic duals of 4d BCFTs comprising 4d $\mathcal N=4$ SYM on a half space coupled to 3d $\mathcal N=4$ SCFTs on the boundary. Based on the concrete BCFTs and their brane construction, we provide microscopic realizations of the intermediate holographic description, obtained by dualizing only the 3d degrees of freedom. Triggered by recent observations in bottom-up models, we discuss the causal structures in the full BCFT duals and intermediate descript…
Boundary conformal field theory, holography and bulk locality
本文研究了在反德西特空间背景中存在终点世界膜（EOW）膜的情况下，标量有效场论（EFT）中的体积局部性。通过边界共形场论（BCFT）的双描述，计算了标量算子的二点相关函数，并将其解析结构与边界共形对称性约束进行比较。结果表明，从局部体积描述导出的修正相关函数与BCFT期望不完全一致，这为双重BCFT构造中的体积局部性提供了非平凡约束，并识别BCFT相关函数作为存在边界时量子体积动力学的敏感探针。
The recent paper 1809.01197 described how states of a holographic CFT can be approximated by states of a large collection of non-interacting BCFTs, such that the dual of the new system accurately approximates an arbitrarily large causal patch of the original geometry. In this paper, we first describe in more detail the geometries dual to such discrete BCFT systems, emphasizing that they are multi-boundary wormholes in which it is not possible to move causally between different asymptotic regions. By reintroducing couplings between the BCFTs in various ways, we show that the wormholes can be ma…
The entanglement wedge cross section in holographic picture provides a geometrical description of the entanglement for mixed states. In this paper we study the inequalities for the entanglement wedge cross section in AdS/BCFT duality. In the presence of the boundary in conformal field theory (CFT), the dual entanglement wedge cross section exhibits abundant phase structures since the extremal surface may end on the brane. We present a universal treatment which is applicable for all the possible phases such that the inequalities for the entanglement wedge cross section can be proved in an algeb…
One-point functions for doubly-holographic BCFTs and backreacting defects
该研究结合超对称局域化与全息方法，推导了由Gaiotto-Witten D3/D5/NS5膜构造的、含大量缺陷自由度的4维$\n\bN=4$ SYM中手征初级算符的一点函数，涉及双全息BCFT等多种理论。
Recently it is found that, due to Weyl anomaly, a background scalar field induces a non-trivial Fermi condensation for theories with Yukawa couplings. For simplicity, the paper consider only scalar type Yukawa coupling and, in the BCFT case, only for a specific boundary condition. In these cases, the Weyl anomaly takes on a simple special form. In this paper, we generalize the results to more general situations. First, we obtain general expressions of Weyl anomaly due to a background scalar and pseudo scalar field in general 4d BCFTs. Then, we derive the general form of Fermi condensation from…
By combining the AdS/BCFT correspondence and the brane world holography, we expect an equivalence relation between a boundary conformal field theory (BCFT) and a gravitational system coupled to a CFT. However, it still remains unclear how the boundary condition of the BCFT is translated in the gravitational system. We examine this duality relation in a two-dimensional setup by looking at the computation of entanglement entropy and energy flux conservation. We also identify the two-dimensional gravity which is dual to the boundary dynamics of a BCFT. Moreover, we show that by considering a grav…
We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e. boundary conformal field theory (BCFT). Our new holography, which may be called AdS/BCFT, successfully calculates the boundary entropy or g-function in two dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g-theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.
Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy
本文研究了2维$T\ar{T}$形变边界共形场论中混合态的反射熵，通过岛和缺陷极值面方案计算了渐近AdS$_3$几何下的结果，验证了两种方案主导阶修正的一致性，并分析了形变对Page曲线的影响。
We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a `boundary central charge' in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that thei…
We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT (BCFT) or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi-)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For BCFTs and…
We use holography to study the spectra of boundary conformal field theories (BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular boundaries that correspond to dynamical end-of-the-world branes in 3-dimensional gravity. Interactions between these branes inform the operator content and the energy spectrum of the dual BCFT. As a proof of concept, we first consider two highly separated branes whose only interaction is taken to be mediated by a scalar field. The holographic computation of the scalar-mediated exchange reproduces a light scalar primary and its global descen…
We give an explicit construction of the complete set of Cardy boundary states that respect the extended chiral algebra for symmetric product orbifolds. The states are labelled by a choice of seed theory boundary states as well as a choice of representations of the symmetric group. At large $N$, we analyze the BCFT data which is relevant for holography, namely the boundary entropy and the one-point functions of single-trace operators. In some cases, typical boundary states are compatible with a bulk description in terms of an End-of-the-World brane along with backreacted matter fields. We discu…
Brane Cosmology from AdS/BCFT
本文研究AdS中带局域标量场的EOW膜含时动力学，推导共形维数约束、证明类时g定理，构建类弗里德曼方程的膜宇宙学模型，分类常势解并揭示其大爆炸创生宇宙的描述能力，还得到超平面附近刘维尔引力有效作用量及boost对称膜解。
Holography for Boundary Lifshitz Field Theory
本文提出边界Lifshitz场论（BLFT）的全息对偶，通过EOW膜边界条件定义两类全息BLFT并推导g定理，计算其基态区间纠缠熵与全息结果在边界极限下一致。
Entanglement inequalities for timelike intervals within dynamical holography
本文在AdS₃-维达雅学说框架下，扩展了之前关于单个类时子区域的研究，验证了非重叠子区域的类时互信息正性及弱单调性，并研究了重叠区间下的纠缠不等式，如阿拉基-利布不等式和强子加性，发现强子加性在这些设置中通常被违反。
Cone Holography with Neumann Boundary Conditions and Brane-localized Gauge Fields
本文通过引入膜局域规范场（包括$U(1)$、$p$-形式和Proca场），构造了满足诺伊曼边界条件的锥形全息模型，并证明了KK引力子质量谱非负及全息$c$-定理成立。
Zoo of Correlation Inequalities in Holography and Beyond
本文研究了全息图中基于测量的经典和量子关联，通过同调框架证明了多种纠缠不等式，包括单调性、多边形关系和强超加性，并验证了其双向版本。
We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography can be obtained by taking the zero-volume limit of holographic defect CFT. Remarkably, it can be regarded as a holographic dual of the edge modes on the defects. For one class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the …
It was recently discovered that for a boundary system in the presence of a background magnetic field, the quantum fluctuation of the vacuum would create a non-uniform magnetization density for the vacuum and a magnetization current is induced in the vacuum. It was also shown that this magnetic Casimir effect of the vacuum is closely related to another quantum effect of the vacuum, the Weyl anomaly. Furthermore, the phenomena can be understood in terms of the holography of the boundary system. In this article, we review the derivation of this phenomena from QFT as well as the derivation of it u…
In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean on-shell action of a (d-1)-brane probing the bulk geometry and the Euclidean gravitational bulk action. This relation is crucial for the consistency of holography, yet it is non-trivial from the bulk perspective. In particular, we show that it relies on a nice isoperimetric inequality that must be satisfied in a large class of Poincaré-Einstein spaces. Remar…
We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity ($d=3$), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reprod…
Entanglement structure in quantum many-body systems, field theories, and holography
本论文发展量子场论、全息与张量网络新技术，研究含质量、相互作用及边界系统的纠缠结构，推广传统全息并给出 AdS/BCFT 局域算符淬灭的正确处方。
Odd entanglement entropy in boundary conformal field theories and holographic moving mirrors
本文通过复制技巧研究（1+1）维边界共形场论中二分混合态的奇纠缠熵，并验证其与AdS$_3$几何中体纠缠楔截面的全息对偶，同时扩展到全息移动镜模型以模拟霍金辐射。
Holographic Bound of Casimir Effect in General Dimensions
该研究将3维边界共形场论Casimir效应的全息下界讨论推广到高维，证明多种引力理论给出条形区域普适下界，还推导了楔形区域的界并验证，表明全息界适用于一般边界形状。
There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confi…
In this work we generalize the entanglement of purification and its conjectured holographic dual to conditional and multipartite versions of the same, where the optimization defining the entanglement of purification is now optimized in either a constrained way or over multiple parties. We separately derive new constraints on both the conditional entanglement of purification and its conjectured holographic dual object that match, further reinforcing the likelihood of this conjecture. We also show that the multipartite objects we define, despite obeying several of the same inequalities, are not …
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed viewpoint of field theory and holography. A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. The structures of the ultraviolet divergences and the universal parts are determined and compared with the holographic descriptions of entanglement entropy. The utility of qu…
Exploring causality in braneworld/cutoff holography via holographic scattering
本研究通过分析体散射过程，提出膜/截断表面信息遵循源自背后虚构边界的诱导光锥传播，从而解决了广义全息中的因果性与熵不等式违反问题。
Toward a Consistent Definition of Holographic Entanglement Entropy in de Sitter Space
本文在德西特静态片全息框架下提出一种新的全息纠缠熵定义，利用复制技巧和扭转算符导出熵泛函，并通过熵不等式约束参数空间，为静态片全息的一致性提供定量支持。
We consider a class of correlation measures for quantum states called optimized correlation measures, defined as a minimization of a linear combination of von Neumann entropies over purifications of a given state. Examples include the entanglement of purification $E_P$ and squashed entanglement $E_{\text{sq}}$. We show that when evaluating such measures on ``nice" holographic states in the large-$N$ limit, the optimal purification has a semi-classical geometric dual. We then apply this result to confirm several holographic dual proposals, including the $n$-party squashed entanglement. Moreover…
In the context of higher-spin holography, we compare the classification of cubic interaction vertices for higher-spin gravity theories in three dimensions to the possible three-point correlation functions of conserved higher-spin currents in two-dimensional conformal field theories. In both cases, the allowed structures are governed by triangle inequalities for the involved spins. It is established that higher-order correlators satisfy similar polygon inequalities and that the same inequalities are valid for higher-order continuations of cubic vertices in the three-dimensional higher-spin grav…
It was recently discovered that for a boundary system in the presence of a background magnetic field, the quantum fluctuation of the vacuum would create a non-uniform magnetization density for the vacuum and a magnetization current is induced in the vacuum. It was also shown that this "magnetic Casimir effect" of the vacuum is closely related to another quantum effect of the vacuum, the Weyl anomaly. Furthermore, the phenomena can be understood in terms of the holography of the boundary system. In this paper, we generalize this four dimensional effect to six dimensions. We use the AdS/BCFT hol…
Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation $ΔS=ΔH$ for the first order variation of the entanglement entropy $ΔS$ and the expectation value of the \modu Hamiltonian $ΔH$. We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check tha…
Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff
本文研究了有限截断AdS/CFT中纠缠楔嵌套（EWN）的约束，发现在ETW膜上定义EW时需满足比EWN更强的类空分离条件，揭示了截断理论的非局域性。
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki $L_p$ spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from (Sutter, Berta \& Tomamichel 2017). Then, using the Haag…
We study properties of the minimal cross section of entanglement wedge which connects two disconnected subsystems in holography. In particular we focus on various inequalities which are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument which supports this identification based on a tensor network interpretation of holography. This implies that the entanglement of purification satisfies the strong superadditivity for holograp…
Constraints on Kasner Exponents from Holography and Energy Conditions
本文通过全息探针（CV、CA、HM熵和热a-函数）对平面AdS黑洞内部的Kasner指数施加代数约束，并证明经典能量条件（零和主能量条件）是这些约束的充分条件，建立了体能量条件与内部几何的直接联系。
Tripartite Form Universality in Holographic Entropy Inequalities
本文猜想并证明两个无限全息熵不等式族均可改写为三部分形式，提供显式表达式并推导有用恒等式，展示该形式在证明结构性质中的威力。
There is some tension between two well-known ideas in holography. On the one hand, subregion duality asserts that the reduced density matrix associated with a limited region of the boundary theory is dual to a correspondingly limited region in the bulk, known as the entanglement wedge. On the other hand, correlators that in the boundary theory can be computed solely with that density matrix are calculated in the bulk via the GKPW or BDHM prescriptions, which require input from beyond the entanglement wedge. We show that this tension is resolved by recognizing that the reduced state is only ful…
It was recently found that the stabilizer and hypergraph entropy cones coincide for four parties, leading to a conjecture of their equivalence at higher party numbers. In this note, we show this conjecture to be false by proving new inequalities obeyed by all hypergraph entropy vectors that exclude particular stabilizer states on six qubits. By further leveraging this connection, we improve the characterization of stabilizer entropies and show that all linear rank inequalities at five parties, except for classical monotonicity, form facets of the stabilizer cone. Additionally, by studying mini…
PEE threads and bit threads in gravitational subregions of AdS
该研究在引力子区域运动学空间描述的基础上，构建了AdS体中PEE线与比特线的新颖构型，揭示了其几何特性，阐明了相关自由度在全息纠缠中的作用，建立了不同理论概念间的联系。
We develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in arXiv:1808.07871, of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic an…
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