Figure 4 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
LEFT: a black hole in AdS that receives a kick at t 0 . Arbitrary trajectories in AdS can be generated by a dense sequence of such instantaneous kicks, allowing us to describe proper time evolution in any weakly curved spacetime. RIGHT: twin black holes. The left twin is static while the right twin is the accelerated black hole of the LEFT panel. The time dilation experienced by the twins is computed by the modular Berry holonomy of the "loop" of modular Hamiltonians describing the two trajectories and the integral of the zero mode projection of the CFT Hamiltonian along the loop via eq. (3.28), (3.29).
Source publication
A bstract
We develop a holographic framework for describing the experience of bulk observers in AdS/CFT, that allows us to compute the proper time and energy distribution measured along any bulk worldline. Our method is formulated directly in the CFT language and is universal: it does not require knowledge of the bulk geometry as an input. When use...
Context in source publication
Similar publications
Inverse Compton scattering sources are finding increasing use as intense sources of high-energy photons. When operated at high field strength, ponderomotive detuning of the scattered emission can lead to decreased source performance. Up to now, the calculations of spectra for such nonlinear Thomson scattering have been done assuming a perfectly ali...
One of the outstanding problems in the holographic approach to many-body physics is the explicit computation of correlation functions in nonequilibrium states. We provide a new and simple proof that the horizon cap prescription of Crossley-Glorioso-Liu for implementing the thermal Schwinger-Keldysh contour in the bulk is consistent with the Kubo-Ma...
Construct-based models have become a mainstay of management and information systems research. However, these models are likely overfit to the data samples upon which they are estimated, making them risky to use in explanatory, prescriptive, or predictive ways outside a given sample. Empirical researchers currently lack tools to analyze why and how...
![The Cosserat couple modulus μc\documentclass[12pt]{minimal}...](publication/363492840/figure/fig2/AS:11431281095006851@1667702939242/The-Cosserat-couple-modulus-mcdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
We consider the classical Mindlin–Eringen linear micromorphic model with a new strictly weaker set of displacement boundary conditions. The new consistent coupling condition aims at minimizing spurious influences from arbitrary boundary prescription for the additional microdistortion field P. In effect, P is now only required to match the tangentia...
Citations
... Using this approach, the time an observer takes to reach the black hole singularity can be extracted from boundary correlators (see [43][44][45] for recent progress). 3 The work of [48,49] studied measurements made along non-geodesic worldlines and the connection between boundary modular time and bulk worldline time. Timelike entanglement entropy on the boundary encodes bulk time along piecewiseextremal surfaces via an analytically-continued version of the Ryu-Takayanagi prescription [50,51]. ...
A classical observer can measure elapsed proper time along their worldline. When observers are coupled to a system with internal correlations, measurements of elapsed time may inherit these correlations. We show that derivatives of the on-shell action with respect to worldline mass compute correlation functions of worldline proper length at tree level. We study worldlines coupled to a scalar field. We calculate the length-length two-point function and find it arises from correlated path fluctuations. As an application, we propose that the logarithm of local correlators serves as a generating function of length correlators, which generalizes the on-shell action prescription. Using this proposal, we extract AdS worldline observables from local CFT correlators as computed by Witten diagrams. We briefly discuss extensions to gravity, interferometers, and the holographic encoding of observer time.
... Entanglement entropy is a critical ingredient also in the formulation of the strong subadditivity paradox for Hawking emission [11][12][13], or in the proof of the generalized second law of thermodynamics [14]. Holographic entanglement entropy beyond the classical formula also requires a definition of entanglement in the bulk [15][16][17][18][19][20][21]; and quantum entanglement entropy is relevant for defining the quantum extremal surface and the proposals for reconstructing bulk observables and the black hole interior [22][23][24][25][26][27][28]. Some of the works implementing the replica method assume absence of tachyons-it would be interesting to explore this in more detail. ...
We analyze the one-loop quantum entanglement entropy in ten-dimensional type-II string theory using the orbifold method by analytically continuing in N the genus-one partition function for string orbifolds on R 2 / Z N conical spaces known for all odd integers N > 1 . We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region 0 < N ≤ 1 resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography.
Published by the American Physical Society 2024
... For spherical spacelike subregions in holographic CFTs they implement a geometric flow of bulk operators within the corresponding bulk entanglement wedges [28,29]. This is why it has already been used extensively in the context of tracking bulk fields for both the pure AdS and AdS black hole backgrounds [16,30,31,13,11,14], including fields inside black hole horizons [32,33,34]. ...
It is well known that the entanglement entropies for spacelike subregions, and the associated modular Hamiltonians play a crucial role in the bulk reconstruction program within anti–de Sitter (AdS) holography. Explicit examples of the Hamilton-Kabat-Lifschytz-Lowe (HKLL) map exist mostly for the cases where the emergent bulk region is the so-called entanglement wedge of the given boundary subregion. However, motivated from the complex pseudoentropy in Euclidean conformal field theories (CFT), one can talk about a ``timelike entanglement'' in Lorentzian CFTs dual to AdS spacetimes. One can then utilize this boundary timelike entanglement to define a boundary ``timelike modular Hamiltonian''. We use constraints involving these Hamiltonians in a manner similar to how it was used for spacelike cases, and write down bulk operators in regions which are not probed by an RT surface corresponding to a single CFT. In the context of two-dimensional CFT, we rederive the HKLL formulas for free bulk scalar fields in three examples: in AdS Poincaré patch, inside and outside of the AdS black hole, and for de Sitter flat slicings. In this method, one no longer requires the knowledge of bulk dynamics for subhorizon holography.
... JT gravity has been a productive test ground for studying of von Neumann algebras in gravity beyond the semiclassical regime [48,49], revealing the importance of different topologies in the description of the algebra of observables. However, the use of the centaur model in our work is not aimed at extending the discussion about the role of topologies, as above, but rather to emphasize the transition in the algebraic description of different subsystems of the semiclassical theory, in particular the TT deformations of the 2D flow geometries, which are expected to be associated with subregions in the bulks; and algebra of operators accessible to an observer given by a protocol according to [50]. ...
... We employ the protocol of [1,50,70] that describes the experience of an infalling observer, modeled as a probe black hole, from the boundary of a generic asymptotically AdS d+1 spacetime, including the centaur geometry. We prepare a microcanonical TFD configuration dual to a black hole geometry and a copy of it, which we refer to as the reference system, with energy eigenstates |E n ⟩ sys and E n ref respectively. ...
... Then, the crossed product algebra could remain type II ∞ instead of II 1 , as traces might include non-normalizable states. Regardless of that, the evolution of the atmosphere operators in the algebra will be JHEP03(2024)008 determined by scrambling modes of the modular Hamiltonian [50]. Moreover, these modes produce null shifts along the horizon of the background black hole [1]. ...
A bstract
This letter explores a transition in the type of von Neumann algebra for asymptotically AdS spacetimes from the implementations of the different gravitational constraints. We denote it as the centaur-algebra of observables. In the first part of the letter, we employ a class of flow geometries interpolating between AdS 2 and dS 2 spaces, the centaur geometries. We study the type II ∞ crossed product algebra describing the semiclassical gravitational theory, and we explore the algebra of bounded sub-regions in the bulk theory following $$ T\overline{T} $$ T T ¯ deformations of the geometry and study the gravitational constraints with respect to the quasi-local Brown-York energy of the system at a finite cutoff. In the second part, we study arbitrary asymptotically AdS spacetimes, where we implement the boundary protocol of an infalling observer modeled as a probe black hole proposed by [1] to study modifications in the algebra. In both situations, we show how incorporating the constraints requires a type II 1 description.
... While the CFTs don't interact, the bulk description of their time evolution involves Alice and Bob meeting and interacting behind the horizon. After being initially emphasized by Marolf and Wall [1], how to understand these behind the horizon interactions as emerging from a boundary perspective has remained puzzling, and many perspectives on this have been offered [2][3][4][5][6][7][8]. ...
... To describe this task succinctly, it is helpful to introduce two agencies, Alice and Bob, who interact to carry out the task. 4 We will label the input locations by C i where Bob gives Alice quantum systems A i . These may be entangled with some reference R, which we take to be held by Bob. ...
A bstract
In a two sided black hole, systems falling in from opposite asymptotic regions can meet inside the black hole and interact. This is the case even while the two CFTs describing each asymptotic region are non-interacting. Here, we relate these behind the horizon interactions to non-local quantum computations. This gives a quantum circuit perspective on these interactions, which applies whenever the interaction occurs in the past of a certain extremal surface that sits inside the black hole and in arbitrary dimension. Whenever our perspective applies, we obtain a boundary signature for these interior collisions which is stated in terms of the mutual information. We further revisit the connection discussed earlier between bulk interactions in one sided AdS geometries and non-local computation, and recycle some of our techniques to offer a new perspective on making that connection precise.
... While it is possible to express bulk operators in the black hole interior regions in terms of boundary operators [18][19][20][21][22], such "bulk reconstructions" require either evolving bulk equations of motion or analytic continuation around the horizon, and thus are not intrinsically boundary constructions. See also [23,24] for an interesting recent discussion of keeping track of the proper time of an in-falling observer using modular flows and [25][26][27][28][29] for a description of the black hole interior from the perspective of coarse graining. ...
In holographic duality an eternal Anti-de Sitter black hole is described by two copies of the boundary Conformal Field Theory in the thermal field double state. In this paper we provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III1 von Neumann algebraic structure from the type I boundary operator algebra and the half-sided modular translation structure associated with it.
... There have been different interesting attempts, such as direct generalizations of the notion of operator size we use here[21][22][23], as well as connections with operator complexity[24][25][26][27][28] and related work on the gravity picture[29][30][31]. ...
A bstract
When two particles collide in an asymptotically AdS spacetime with high enough energy and small enough impact parameter, they can form a black hole. Motivated by dual quantum circuit considerations, we propose a threshold condition for black hole formation. Intuitively the condition can be understood as the onset of overlap of the butterfly cones describing the ballistic spread of the effect of the perturbations on the boundary systems. We verify the correctness of the condition in three bulk dimensions. We describe a six-point correlation function that can diagnose this condition and compute it in two-dimensional CFTs using eikonal resummation.
... This operational point of view has been undertaken e.g. in[19]. ...
Quantum gravitational effects can become important at low energy if the wavefunction of the metric field fails to be peaked around a classical configuration. We try to understand such deviations from classicality within canonical quantum gravity by introducing a “fluid of observers” in the low energy theory and defining a distance operator “at equal time” among them. We find that, even in the presence of relevant fluctuations in the metric field, a “locally flat” limit is recovered in the neighbourhood of each observer. Deviations from classicality have no particular consequence, locally. However, at larger separations the expectation value of the distance operator behaves differently than a standard Riemannian distance. In particular, it is non-additive and thus cannot be obtained by the integral of a differential line element. This emerging “beyond Riemannian” geometry is a metric space similar to embedded Riemannian manifolds equipped with chord distances that “cut through” the ambient space. We study deviations from flat space by looking at triangles in the limit where their sizes go to zero. Beyond-Riemannian deviations with respect to flat space are of the same order as standard Riemannian ones, but qualitatively different. Possible connections with holography and with the black hole information paradox are briefly discussed.
... We employ the protocol of [1,64,65] that describes the experience of an infalling observer, modeled as a probe black hole, from the boundary of a generic asymptotically AdS d+1 spacetime, including the centaur geometry. We prepare a microcanonical TFD configuration dual to a black hole geometry and a copy of it, which we refer to as the reference system, with energy eigenstates |E n sys and E n ref respectively. ...
... Then, the crossed product algebra could remain type II ∞ instead of II 1 , as traces might include non-normalizable states. Regardless of that, the evolution of the atmosphere operators in the algebra will be determined by scrambling modes of the modular Hamiltonian [64]. Moreover, these modes produce null shifts along the horizon of the background black hole [1]. ...
This letter explores a transition in the type of the von Neumann algebra for spacetimes that interpolates between an open and a closed universe from the implementations of the different gravitational constraints. We denote it as the \emph{centaur-algebra} of observables. Specifically, we employ a class of flow geometries interpolating between AdS$_2$ and dS$_2$ spaces, the centaur geometries. We study the type II$_\infty$ crossed product algebra describing the semiclassical gravity theory and consider two modifications. In the former, we explore bounded sub-regions in the bulk theory following $T\overline{T}$ deformations of the geometry and implement the constraints with respect to the quasi-local Brown-York energy of the system at a finite cutoff. In the latter, we implement the boundary protocol of an infalling observer modeled as a probe black hole arXiv:2211.16512 to study modifications in the algebra. In both situations, we show how incorporating the constraints requires a type II$_1$ description, and we analyze the generality of the results.
... An alternative viewpoint is that the observer could arise as an external degree of freedom that is consistently coupled to the gravitational theory. For example, a holographic model for a bulk observer as a probe black hole was described in [145,146]. The black hole arises via entangling the CFT with a reference system, and hence one could interpret the reference system as the extra degree of freedom associated with the observer. ...
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II$_1$, implying the existence of an entropy maximizing state, which realizes a version of Jacobson's entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose modular flow is geometric at an instant in time. Our results generalize the recent work of Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the static patch of de Sitter space.
