Bulk Reconstruction Research Articles

Magnetic braneworlds: cosmology and wormholes

We construct 4D flat Big Bang-Big Crunch cosmologies and Anti-de Sitter (AdS) planar eternally traversable wormholes using braneworlds embedded in asymptotically AdS5 spacetimes. The background geometries are the AdS5 magnetic black brane and the magnetically charged AdS5 soliton, respectively. The two setups arise from different analytic continuations of the same saddle of the gravitational Euclidean path integral, in which the braneworld takes the form of a Maldacena-Maoz Euclidean wormhole. We show the existence of a holographic dual description of this setup in terms of a microscopic Euclidean boundary conformal field theory (BCFT) on a strip. By analyzing the BCFT Euclidean path integral, we show that the braneworld cosmology is encoded in a pure excited state of a CFT dual to a black brane microstate, whereas the braneworld wormhole is encoded in the ground state of the BCFT. The latter confines in the IR, and we study its confining properties using holography. We also comment on the properties of bulk reconstruction in the two Lorentzian pictures and their relationship via double analytic continuation. This work can be interpreted as an explicit, doubly-holographic realization of the relationship between cosmology, traversable wormholes, and confinement in holography, first proposed in arXiv:2102.05057, arXiv:2203.11220.

Bulk reconstruction from generalized free fields

We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided SYK models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the TFD state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the shockwave geometry and the traversable wormhole geometry using the two-sided mutual information between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk.

Relational bulk reconstruction from modular flow

The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion A¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{A} $$\\end{document}, operators acting on the bulk qudit can be reconstructed as CFT operators on A¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{A} $$\\end{document}. This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion A. In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary region A, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of A, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a “measurement-based” setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

Geometric surprises in the Python's lunch conjecture

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python’s lunch conjecture of Brown et al., the bulge’s area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS_p× S^qp×Sq. These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.

Bulk reconstruction in flat holography

In this note, we discuss the bulk reconstruction of massless free fields in flat space from the highest-weight representation of boundary Carrollian conformal field theory (CCFT). We expand the bulk field as a sum of infinite descendants of a primary state defined in the boundary CCFT, and discuss the Lorentz invariant bulk-boundary propagator in detail for the BMS3/CCFT2 case. In our calculation, it is necessary to introduce a nonzero mass at the beginning and take it as vanishing at the end. The framework we proposed has the potential to probe local bulk physics from the boundary CCFT.

Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence

Abstract In this paper, we extend the surface growth approach for bulk reconstruction into the AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. In addition, we find that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Furthermore, we also investigate the entanglement of purification within the surface growth process, which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.

Enriched supercapacitive performance of electrochemically tailored β-Co(OH)2/CoOOH nanodiscs from sacrificial Co3(PO4)2·4H2O microbelts

Electrochemically induced structural reconstruction process of metal precursors into their corresponding metal hydroxides/(oxy)hydroxides is developed as an ingenious strategy towards preparing efficient electrode material. However, the influence of electrochemical activation on the charge storage ability of electrode material is barely explored. Herein, we have utilized a synthetic strategy (solvothermal reaction in water:ethanol mixture) to prepare Co3(PO4)2·4H2O microbelts and subsequently applied the electrochemical bulk reconstruction process in 1 M KOH electrolyte. A thorough physical and electrochemical characterization unveil that the electrode material is converted into redox active site rich β-Co(OH)2/CoOOH nanodiscs via etching of lattice anionic PO43− moieties. The material possesses a specific capacitance of 386 F g−1at a current density of 0.25 A g−1. Additionally, a hybrid device constructed with β-Co(OH)2/CoOOH nanodiscs and activated charcoal (AC) as positive and negative electrodes has achieved a high energy density of 13.33 Wh Kg−1at a power density of 400 W kg−1. Further, the device displayed a good capacitance retention of 93 % (columbic efficiency ~98 %) up to 10,000 cycles. The improved charge storage of reconstructed material with abundant redox active sites could be attributed to the facile diffusion of electrolyte ions into the bulk of the material.

Bulk reconstruction using timelike entanglement in (A)dS

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. Published by the American Physical Society 2024

Atomic Reconstruction of Au Thin Films through Interfacial Strains.

Interfaces play a critical thermodynamic role in the existence of multilayer systems. Due to their utility in bridging energetic and compositional differences between distinct species, the formation of interfaces inherently creates internal strain in the bulk due to the reorganization needed to accommodate such a change. We report the effect of scaling interfacial stress by deposition of different adlayers on a host thin metal film. Intrinsic property differences between host and deposited metal atoms result in varying degree of composition and energy gradient within the interface. Interfacial stress can increase defects in the host leading to (i) energy dissipation and reorganization to minimize surface energy, and (ii) increased material strength. We infer that dissipation of interfacial stress induces defect migration, hence bulk and surface atomic reconstruction as captured by the surface roughness and grain size reduction coupled with a concomitant increase in material strength.

Twice upon a time: timelike-separated quantum extremal surfaces

The Python’s Lunch conjecture for the complexity of bulk reconstruction involves two types of nonminimal quantum extremal surfaces (QESs): bulges and throats, which differ by their local properties. The conjecture relies on the connection between bulk spatial geometry and quantum codes: a constricting geometry from bulge to throat encodes the bulk state nonisometrically, and so requires an exponentially complex Grover search to decode. However, thus far, the Python’s Lunch conjecture is only defined for spacetimes where all QESs are spacelike-separated from one another. Here we explicitly construct (time-reflection symmetric) spacetimes featuring both timelike-separated bulges and timelike-separated throats. Interestingly, all our examples also feature a third type of QES, locally resembling a de Sitter bifurcation surface, which we name a bounce. By analyzing the Hessian of generalized entropy at a QES, we argue that this classification into throats, bulges and bounces is exhaustive. We then propose an updated Python’s Lunch conjecture that can accommodate general timelike-separated QESs and bounces. Notably, our proposal suggests that the gravitational analogue of a tensor network is not necessarily the time-reflection symmetric slice, even when one exists.

Progress in the lattice evaluation of entanglement entropy of three-dimensional Yang-Mills theories and holographic bulk reconstruction

A construction of a gravity dual to a physical gauge theory requires confronting data. We establish a proof-of-concept for precision holography, i.e., the explicit reconstruction of the dual background metric functions directly from the entanglement entropy (EE) of strip subregions that we extract from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on a three-dimensional Euclidean SU2 theory in the deconfining phase. Holographic EE suggests, and we find evidence for, that the scaling of the thermal entropy with temperature is to power 7/3 and that it approaches smoothly the critical point, consistent with black hole thermodynamics. In addition, we provide frugal results on the potential between quenched quarks by the computation of the Polyakov loop correlators on the lattice. Holographic arguments pique curiosity in the substratum of Debye screening at strong coupling.

Nonperturbative gravity corrections to bulk reconstruction

We introduce a new algebraic framework for understanding nonperturbative gravitational aspects of bulk reconstruction with a finite or infinite-dimensional boundary Hilbert space. We use relative entropy equivalence between bulk and boundary with an inclusion of nonperturbative gravitational errors, which give rise to approximate recovery. We utilize the privacy/correctability correspondence to prove that the reconstruction wedge, the intersection of all entanglement wedges in pure and mixed states, manifestly satisfies bulk reconstruction. We explicitly demonstrate that local operators in the reconstruction wedge of a given boundary region can be recovered in a state-independent way for arbitrarily large code subspaces, up to nonperturbative errors in GN . We further discuss state-dependent recovery beyond the reconstruction wedge and the use of the twirled Petz map as a universal recovery channel. We discuss our setup in the context of quantum islands and the information paradox.

Microscopic entanglement wedges

We study the holographic duality between the free O(N) vector model and higher spin gravity. Conserved spinning primary currents of the conformal field theory (CFT) are dual to spinning gauge fields in the gravity. Reducing to independent components of the conserved CFT currents one finds two components at each spin. After gauge fixing the gravity and then reducing to independent components, one finds two components of the gauge field at each spin. Collective field theory provides a systematic way to map between these two sets of degrees of freedom, providing a complete and explicit identification between the dynamical degrees of freedom of the CFT and the dual gravity. The resulting map exhibits many features expected of holographic duality: it provides a valid bulk reconstruction, it reproduces insights expected from the holography of information and it provides a microscopic derivation of entanglement wedge reconstruction.

On the emergence of gravitational dynamics from tensor networks

Tensor networks are used to describe the ground state wavefunction of the quantum many-body system. Recently, it has been shown that a tensor network can generate the anti-de Sitter (AdS) geometry by using the entanglement renormalization approach, which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence. However, whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem. In this paper, we give a novel proposal to integrate ideas from tensor networks, entanglement entropy, canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.

Bulk reconstruction of AdSd+1 metrics and developing kinematic space

The metrics of the global, Poincaré, and Rindler AdSd+1 are explicitly reconstructed with given lightcone cuts. We first compute the metric up to a conformal factor with the lightcone cuts method introduced by Engelhardt and Horowitz. While a general prescription to determine the conformal factor is not known, we recover the factor by identifying the causal information surfaces from the lightcone cuts and finding that they are minimal. In addition, we propose a new type of kinematic space as the space of minimal surfaces in AdSd+1, where a metric is introduced as a generalization of the case of d = 2. This metric defines the set of bulk points, which is equivalent to that of lightcone cuts. Some other properties are also studied towards establishing a reconstruction procedure for general bulk metrics.

Toward random tensor networks and holographic codes in CFT

In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.

Extension of the HKLL bulk reconstruction for small ∆

We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS spacetime, both for the case of even and odd dimensions, for an extended range of conformal dimensions where the original HKLL reconstruction has to be modified. We also discuss the use of space-like Green’s functions in the bulk reconstruction. We demonstrate that in the extended range also the singular part of the Green’s function, omitted in the original papers, has be included. The results are particularly simple and physically interesting for integer conformal dimensions below the range considered in the original HKLL papers.

Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

We study minimum area surfaces associated with a region, R, of an internal space. For example, for a warped product involving an asymptotically AdS space and an internal space K, the region R lies in K and the surface ends on ∂R. We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region R. When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory. We study several examples, including warped or direct products involving AdS2, or higher dimensional AdS spaces, with the internal space, K = Rm, Sm; Dp brane geometries and their near horizon limits; and several geometries with a UV cut-off. We find that such RT surfaces often exist and can be useful probes of the system, revealing information about finite length correlations, thermodynamics and entanglement. We also make some preliminary observations about the role such surfaces can play in bulk reconstruction, and their relation to subalgebras of observables in the boundary theory.

Simple bulk reconstruction in anti-de Sitter/conformal field theory correspondence

Abstract In this paper, we show that bulk reconstruction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is rather simple and has an intuitive picture, by showing that the HKLL (Hamilton-Kabat-Lifschytz-Lowe) bulk reconstruction formula can be simplified. We also reconstruct the wave packets in the bulk theory from the CFT primary operators. With these wave packets, we discuss the causality and duality constraints and find our picture is the only consistent one. Our picture of the bulk reconstruction can be applied to the asymptotic AdS spacetime.

Entanglement islands, fire walls and state paradox from quantum teleportation and entanglement swapping

Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. The formula of generalized entropy derived from the gravitational path integration, nevertheless, does not provide a concrete insight on how information comes out from a black hole. In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands. We propose an identification of entanglement islands with quantum measurements and remark on the parallel between the black hole information problem and the old problem of quantum measurements. We show that the Page curve can still be realized even if information is lost so that the information paradox can be explained as one manifestation of measurement problem. We show that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and demonstrate explicitly that Page curves of solvable 2D gravity can be obtained through teleportation and entanglement swapping. We argue that the similarities between the black hole information problem and the measurement problem suggest links in the origins of the two problems.