Mehrdad Mirbabayi
Replica geometries are not rigid when gravity is dynamical. We numerically construct $1<n\leq 2$ replica saddles in $2d$ gravity coupled to a CFT and compare the resulting Renyi entropies with the field theory result.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number $n \to 1$, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these repl…
The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2$d$ conformal field theory (CFT) description, namely, the Liouville theory coupled to the $(2,p)$ minimal matter in the $p\to\infty$ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the b…
Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking's paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the qua…
We argue that the `island conjecture' and the replica wormhole derivation of the Page curve break monogamy of entanglement through allowing black hole interior states to be non-classically correlated while also pairwise entangled with radiation states. The reason is that quantum degrees of freedom (present in any half of a Hawking pair) cannot all be identified with the environment at semi-classical pair production, and can only be fixed relative to a subsystem, as required for the Page curve, by correlations equivalent to entanglement - regardless of what those correlations are attributed to.…
We study the replica symmetry breaking (RSB) in the Gaussian Unitary Ensemble (GUE) random matrix model. We find that the RSB occurs at the transition temperature $T_{\text{RSB}}\sim N^{-2/3}$ in the large $N$ limit. We argue that this transition originates from a landscape of almost degenerate local minima of free energy labeled by Young diagrams. We also discuss a possible implication of our findings for the multiply-coupled Sachdev-Ye-Kitaev models and their holographic dual Jackiw-Teitelboim gravity from the viewpoint of ER=EPR conjecture.
We define bit models of evaporating black holes which incorporate the effects of replica wormholes. These enter as non-perturbative corrections to the gravitational inner product, arising from spacetime wormholes that connect replica black holes. The resulting models have exactly unitary evolution, predict measurements on Hawking radiation in accord with a Page curve for entropy, and are compatible with a smooth horizon for infalling observers.
It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give $\mathcal{O}(1)$ contributions to the relative entropy after the Page time. Furthermore, using "island" formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples.…
In a 1+1 dimensional QFT on a circle, we consider the von Neumann entanglement entropy of an interval for typical pure states. As a function of the interval size, we expect a Page curve in the entropy. We employ a specific ensemble average of pure states, and show how to write the ensemble-averaged Renyi entropy as a path integral on a singular replicated geometry. Assuming that the QFT is a conformal field theory with a gravitational dual, we then use the holographic dictionary to obtain the Page curve. For short intervals the thermal saddle is dominant. For large intervals (larger than half …
Replica wormhole as a vacuum-to-vacuum transition
本文从热混合双重态与自发对称性破缺视角研究复制虫洞，提出其是不同简并真空间的跃迁、配分函数受简并真空流形支配，经二维Jackiw-Teitelboim引力验证，并关联软毛测量过程。
We study the behavior of Rényi entropies for pure states from standard assumptions about chaos in the high-energy spectrum of the Hamiltonian of a many-body quantum system. We compute the exact long-time averages of Rényi entropies and show that the quantum noise around these values is exponentially suppressed in the microcanonical entropy. For delocalized states over the microcanonical band, the long-time average approximately reproduces the equilibration proposal of H. Liu and S. Vardhan, with extra structure arising at the order of non-planar permutations. We analyze the equilibrium approxi…
Replica Wormholes and Quantum Hair
本文比较副本虫洞与量子毛发两种方法，说明黑洞幺正蒸发中辐射态为时空背景的宏观叠加，且无需跨视界非局域性即可由辐射模式编码内部信息。
In a close look at the replica wormhole derivation of the island conjecture, we note a discrepancy in the derived matrix eigenvalues in the limit where the Hawking radiation entropy goes to zero. The small corrections to the density matrix for the radiation infer that ${\rm tr}(ρ_\textsf{R}^2)$, equally a sum over the eigenvalues squared, must be small ($\ll1$) at all times. This is in contradiction with an ensemble dominated by a density matrix with an eigenvalue close to unity. Also, the radiation entropy has been approximated by the ensemble averaged entropy, as in a final state analysis. F…
Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Rényi entropy of the Sachdev-Ye-Kitaev (SYK) model ($χ$) coupled to a Majorana chain bath ($ψ$). The system is prepared in the thermofield double (TFD) state and then evolved by $H_L+H_R$. For small system-bath coupling, we find that the second Rényi entropy $S^{(2)}_{χ_L, χ_R}$ of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corr…
Euclidean wormholes -- geometries which connect disconnected boundaries -- present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies, and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CG…
Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
本文提出耗散SYK模型作为最小量子模型，展示其纠缠动力学呈现类似副本虫洞的特征，并在大N弱耗散下观察到一阶纠缠跃迁，为量子模拟器研究副本虫洞物理铺路。
Replica wormhole and AMPS firewall
研究 replica wormhole 拓扑在黑洞蒸发 Page 时间后产生 AMPS firewall 的机制，发现事件视界处存在与粒子能量平方成正比的狄拉克δ力，并提出正则化方案，同时解决信息悖论与纠缠单配性论证。
Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for ent…
We investigate contributions of spacetime wormholes, describing baby universe emission and absorption, to calculations of entropies and correlation functions, for example those based on the replica method. We find that the rules of the "wormhole calculus," developed in the 1980s, together with standard quantum mechanical prescriptions for computing entropies and correlators, imply definite rules for $\textit{limited}$ patterns of connection between replica factors in simple calculations. These results stand in contrast with assumptions that all topologies connecting replicas should be summed o…
Page curves and replica wormholes from random dynamics
本文在一个具有GUE随机哈密顿量的玩具量子系统中，通过区分平均态熵与平均熵，揭示了非幺正佩奇曲线与恢复幺正性的类副本虫洞贡献之间的差异来源。
Recent work has shown how to understand the Page curve of an evaporating black hole from replica wormholes. However, more detailed information about the structure of its quantum state is needed to fully understand the dynamics of black hole evaporation. Here we study entanglement negativity, an important measure of quantum entanglement in mixed states, in a couple of toy models of evaporating black holes. We find four phases dominated by different types of geometries: the disconnected, cyclically connected, anti-cyclically connected, and pairwise connected geometries. The last of these geometr…
We show that the presence of replica wormholes in the Euclidean path integral of gravity leads to a non-perturbative violation of charge conservation for any global symmetry present in the low-energy description of quantum gravity. Explicitly, we compute the scattering probability between different charged states in several two-dimensional models of quantum gravity and find a non-vanishing answer. This suggests that the set of all charged states is typically over-complete, which has drastic consequences for the fate of black hole remnants that could carry a global symmetry charge. In the holog…
Counting states in a model of replica wormholes
本研究针对复制虫洞诱导内积的多黑洞系统希尔伯特空间，通过规范对称性解读置换求和形式，借助大n极限下的涌现库仑气体描述计数态，发现三阶相变并验证其维度符合贝肯斯坦-霍金熵的微观解释。
Black Hole Information, Replica Wormholes, and Macroscopic Entanglement
本文综述了黑洞蒸发产生的宏观纠缠霍金辐射，指出复制虫洞与量子毛发效应支持其纯态性质，并利用宏观纠缠解决信息悖论。
We consider the capacity of entanglement as a probe of the Hawking radiation in a two-dimensional dilaton gravity coupled with conformal matter of large degrees of freedom. A formula calculating the capacity is derived using the gravitational path integral, from which we speculate that the capacity has a discontinuity at the Page time in contrast to the continuous behavior of the generalized entropy. We apply the formula to a replica wormhole solution in an eternal AdS black hole coupled to a flat non-gravitating bath and show that the capacity of entanglement is saturated by the thermal capac…
Replica Rényi Wormholes and Generalised Modular Entropy in JT Gravity
该研究在JT引力框架下计算AdS₂背景中CFT的半经典雷尼熵，验证广义模熵极值化与QES条件的一致性，用富克斯单值化理论描述复制虫洞并求解n=2情形，得到高温下双侧永恒黑洞雷尼熵的n依赖Page时间。
The JLMS formula relates the bulk and boundary relative entropies and is fundamental to the holographic dictionary, providing justification for entanglement wedge reconstruction. We revisit the replica trick for relative entropy and find corrections of the JLMS formula in a variety of scenarios, even after accounting for effects of quantum extremality. We analyze the problem in the PSSY model, a model of Jackiw-Teitelboim gravity coupled to end-of-the-world branes. We find non-perturbative (in $G$) corrections that are always present, arising from subdominant replica wormhole gravitational sad…
We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ Rényi entropy includes a wormhole between the $n$ copies of the gravitating universe, leading to a standard "island formula" for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with $2n$ boundaries connecting replica copies of both universes. The anal…
It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-$c$ BCFT Ensemble
直接从对偶二维CFT推导3D引力的RT公式，揭示多区间纠缠与复本虫洞涌现，证明体时空几何源于大c极限下的本征态热化假说（ETH）。
Based on the rigid positive energy theorem we proved the uniqueness of static spherically symmetric traversable wormholes with two asymptotically flat ends, being the higher-dimensional solutions of Einstein scalar phantom field. The proof is valid under the auxiliary condition imposed on wormhole mass and scalar charge.
We examine an interesting set of recent proposals describing a `wormhole paradigm' for black holes. These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon. We prove the `effective small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside. This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation. We try to illustrat…
Studying replica wormholes and the Page curve with simplicial quantum gravity
本文基于量子 Regge 微积分（QRC）开发了单纯量子引力框架，通过引入同时容纳引力与辐射自由度的三角剖分方案，在受控微超空间约化中重现了 Page 跃迁，为复本方法超越 JT 引力等现有模型提供了有希望的基础。
Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity
本研究通过复制技巧分析EoW与岛屿模型中复制参数对模熵和纠缠容量的影响，发现更多连通几何能纯化热霍金辐射，并推广岛屿公式至有限n情形。
This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our f…
Replica Wormholes and Entanglement Islands in the Karch-Randall Braneworld
本文推导了Karch-Randall膜世界中的量子极值面公式及其几何化，证明Ryu-Takayanagi曲面的拓扑相变对应于膜上复本虫洞的形成，从而给出与幺正性一致的Hawking辐射Page曲线，并推广讨论了高维情况下膜几何满足的Einstein方程及其对引力路径积分的推论。
In this paper, we study the entanglement entropy between two SYK systems with bilinear coupling. We use the replica trick to calculate the entanglement entropy in the ground state. In parallel, we calculate the entanglement entropy through the Ryu-Takayanagi formula in gravity. For the ground state that is dual to an eternal traversable wormhole in AdS_2, the bulk quantum correction to the entanglement entropy is of the same order as the minimal surface area. The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entangl…
We reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the as…
Replica Phase Transition with Quantum Gravity Corrections
研究近极端Reissner-Nordström黑洞近视界波动的边界有效理论，揭示温度和耦合常数控制的相变结构。
We set up a new version of black hole information paradox in an eternal Narayan black hole, a generic two-dimensional dilaton gravity theory with non-trivial on-shell bulk action and a product of dimensional reduction from higher-dimensional AdS black brane, joined to Minkowski bath on both sides. We also report both similarities as well as important differences between our model and the famous model of JT gravity coupled with baths. The contradiction of Hawking's result of entanglement entropy with unitarity is resolved by including a new saddle in the Euclidean gravitational path integral. A…
Naively, a resolution of the black hole information paradox appears to involve microscopic details of a theory of quantum gravity. However, recent work has argued that a unitary Page curve can be recovered by including novel replica instantons in the gravitational path integral. Moreover, replica instantons seem to rely on disorder averaging the microscopic theory, without a definite connection to a single, underlying unitary quantum system. In this letter, we show that disorder averaging and replica instantons emerge naturally from a gravitational effective theory built out of typical microsc…
Aspects of the low energy physics of certain Jackiw-Teitelboim gravity and supergravity theories are explored, using their recently presented non-perturbative description in terms of minimal string models. This regime necessarily involves non-perturbative phenomena, and the inclusion of wormhole geometries connecting multiple copies of the nearly AdS$_2$ boundary in the computation of ensemble averages of key quantities. A new "replica-scaling" limit is considered, combining the replica method and double scaling with the low energy limit. Using it, the leading free energy, entropy, and specifi…
Quantum Black Holes and Gauge/Gravity Duality
本研究探讨量子引力中黑洞信息丢失悖论，通过AdS/CFT对应框架，结合广义纠缠熵、量子极值表面等方法，揭示信息恢复机制。
The Hubeny-Rangamani-Takayanagi surface $γ_{HRT}$ computing the entropy $S(D)$ of a domain of dependence $D$ on an asymptotically AdS boundary is known to be causally inaccessible from $D$. We generalize this gravitational result to higher replica numbers $n >1$ by considering the replica-invariant surfaces (aka `splitting surfaces') $\boldsymbol{\mathbfγ}$ of real-time replica-wormhole saddle-points computing Rényi entropies $S_n(D)$ and showing that there is a sense in which $D$ must again be causally inaccessible from $\boldsymbol{\mathbfγ}$ when the saddle preserves both replica and conjug…
A Black Hole Airy Tail
针对JT引力中淬火熵计算依赖难以理解的副本极限的问题，本文提出半淬火熵中间量，通过体、边界两种方法计算并验证一致性，阐明单特征值瞬子鞍点的适用局限，为黑洞基态研究提供路径积分方法支撑。
Algebras and States in JT Gravity
该研究分析了JT引力中边界可观测量的代数结构，揭示了含物质时的II∞型非交换代数特性，验证了熵的代数定义与复制技巧的一致性，并探讨了虫洞对体希尔伯特空间与边界态空间关系的影响。
de Sitter space is sometimes not empty
本文通过 dS-AdS 纠缠场论与复制虫洞计算证明，仅当 de Sitter 视界熵大于 AdS 黑洞熵时，其 Hilbert 空间才有效非平凡。
Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity
本文探讨了在 JT 引力中，通过纠缠容量探测岛屿结构的额外信息，揭示了即使熵保持不变，纠缠容量仍能提供有限 n 的信息。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。