Holographic Spacetime Research Articles

Inverse problem of correlation functions in holography

This paper shows that the bulk metric of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of two probe scalar operators by solving Gel’fand-Levitan-Marchenko integral equation. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes a new method to “measure” the corresponding holographic spacetime for a material that has holographic dual but also provides an approach to experimentally check if a system has holographic dual.

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.

Constraints on physical computers in holographic spacetimes

Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on nn qubits which cannot be implemented inside of black holes with entropy less than O(2^n)O(2n). To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

Renormalisation group flows of deformed SYK models

We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, q and q~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overset{\\sim }{q} $$\\end{document}, of interacting fermions. In the large N limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large q limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS2 spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS2 region in the deep interior resides entirely within the geometric regime.

From complexity geometry to holographic spacetime

From complexity geometry to holographic spacetime

Shooting null geodesics into holographic spacetimes

We find, in the AdS/CFT, a source on the boundary which generates one wave packet drawing a null geodesic inside the bulk. Once such a wave packet dives into the bulk, it comes back to the boundary after a specific time, at which the expectation value of the corresponding boundary operator finally stands up. Since this behavior strongly reflects the existence of the holographic spacetime, our technique will be helpful in identifying holographic materials.

Spacetime-emergent ring toward tabletop quantum gravity experiments

We propose a way to discover, in tabletop experiments, spacetime-emergent materials, that is, materials holographically dual to higher-dimensional quantum gravity systems under the AdS/CFT. The emergence of the holographic spacetime is verified by a mathematical imaging transform of the response function on the material. We consider theories on a one-dimensional ring-shaped material and compute the response to a scalar source locally put at a point on the ring. When the theory on the material has a gravity dual, the imaging in the low-temperature phase exhibits a distinct difference from the ordinary materials: The spacetime-emergent material can look into the holographically emergent higher-dimensional curved spacetime and provides an image as if a wave had propagated there. Therefore the image is an experimental signature of the spacetime emergence. We also estimate the temperature, ring size, and source frequency usable in experiments, with an example of a quantum critical material, ${\mathrm{TlCuCl}}_{3}$.

A unified model of inflation and dark energy based on the holographic spacetime foam

I present a model of inflation and dark energy in which the inflaton potential is constructed by imposing that a scalar field representing the classical energy of the spacetime foam inside the Hubble horizon is an exact solution to the cosmological equations. The resulting potential has the right properties to describe both the early and late expansion epochs of the universe in a unified picture.

Renormalization group flow to effective quantum mechanics in the IR in an emergent dual holographic description for spontaneous chiral symmetry breaking

Implementing the Wilsonian renormalization group (RG) transformation in a nonperturbative way, we construct an effective holographic dual description with an emergent extradimension identified with an RG scale. Taking the large$-N$ limit, we obtain an equation of motion of an order-parameter field, here the chiral condensate for our explicit demonstration. In particular, an intertwined structure manifests between the first-order RG flow equations of renormalized coupling functions and the second-order differential equation of the order-parameter field, thus referred to as a nonperturbative RG-improved mean-field theory. Assuming translational symmetry as a vacuum state, we solve these nonlinear coupled mean-field equations based on a matching method between UV- and IR-regional solutions. As a result, we find an RG flow from a weakly-coupled chiral-symmetric UV fixed point to a strongly-correlated chiral-symmetry broken IR fixed point, where the renormalized velocity of Dirac fermions vanishes most rapidly and effective quantum mechanics appears at IR. Furthermore, we translate these RG flows of coupling functions into those of emergent metric tensors and extract out geometrical properties of the emergent holographic spacetime constructed from the UV- and IR-regional solutions. Surprisingly, we obtain the volume law of entanglement entropy in the Ryu-Takayanagi formula, which implies appearance of a black hole type solution in the limit of infinite cutoff even at zero temperature. We critically discuss our field theoretic interpretation for this solution in terms of potentially gapless multi-particle excitation spectra.

Holographic space-time, Newton’s law, and the dynamics of horizons

Holographic space-time, Newton’s law, and the dynamics of horizons

Discretely Charged Dark Matter in Inflation Models Based on Holographic Space-Time

The holographic space-time (HST) model of inflation has a potential explanation for dark matter as tiny primordial black holes. Motivated by a recent paper of Barrau, we propose a version of this model where some of the inflationary black holes (IBHs), whose decay gives rise to the Hot Big Bang, carry the smallest value of a discrete symmetry charge. The fraction f of IBHs carrying this charge is difficult to estimate from first principles, but we determine it by requiring that the crossover between radiation and matter domination occurs at the correct temperature Teq∼1eV=10−28MP. The fraction is small, f∼2×10−9, so we believe this gives an extremely plausible model of dark matter.

Holographic cone of average entropies

The holographic entropy cone identifies entanglement entropies of field theory regions, which are consistent with representing semiclassical spacetimes under gauge/gravity (holographic) duality. It is currently known up to five regions. Here we point out that average entropies of p-partite subsystems can be similarly analyzed for arbitrarily many regions. We conjecture that the holographic cone of average entropies is simplicial and specify all its bounding inequalities and extreme rays, which combine features of perfect tensor and bipartite entanglement. Heuristically, the conjecture posits that bipartite entanglement achieves the most efficient purification consistent with a holographic spacetime interpretation. We also explain that the extreme forms of entanglement allowed by our conjecture are realized by evaporating black holes.

Crossing Versus Locking: Bit Threads and Continuum Multiflows

Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu–Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. We investigate for which choices of bound a given set of boundary regions can be “locked”, in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

Holographic spacetime, black holes and quantum error correcting codes: a review

This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

The holographic space-time and black hole remnants as dark matter

The holographic space-time approach to inflation provides a well defined and self-contained framework to study the early universe. Based on a quasi-local quantum gravity theory generalizing string theory beyond AdS backgrounds, it addresses fundamental questions like the arrow of time and the entropy of the initial cosmological state. It was recently argued that it also provides a natural explanation for dark matter in the form of primordial black holes. The original idea however suffers from troubles that can be cured by considering instead Planck relics. This possibility is investigated and paths for observational confirmation are pointed out.

Holographic spacetime from lattice Yang-Mills theory

Entanglement entropy is a notoriously difficult quantity to compute in strongly interacting gauge theories. Existing lattice replica methods have suffered from a severe signal-to-noise ratio problem, making high-precision studies prohibitively expensive. Our improved lattice method mitigates this situation and allows us to probe holographic predictions for the behavior of entanglement entropies in three- and four-dimensional Yang-Mills theories. We use this data for the numerical reconstruction of holographic bulk metrics.

A Unified Model of Inflation and Dark Energy Based on the Holographic Spacetime Foam

A Unified Model of Inflation and Dark Energy Based on the Holographic Spacetime Foam

Hyperthreads in holographic spacetimes

We generalize bit threads to hyperthreads in the context of holographic spacetimes. We define a “k-thread” to be a hyperthread which connects k different boundary regions and posit that it may be considered as a unit of k-party entanglement. Using this new object, we show that the contribution of hyperthreads to calculations of holographic entanglement entropy are generically finite. This is accomplished by constructing a surface whose area determines their maximum allowed contribution. We also identify surfaces whose area is proportional to the maximum number of k-threads, motivating a possible measure of multipartite entanglement. We use this to make connections to the current understanding of multipartite entanglement in holographic spacetimes.

Do They Compute? Dawn of a New Paradigm based on the Information-theoretic View of Black holes, Universe and Various Conceptual Interconnections of Fundamental Physics

The article endeavors to show how thinking about black holes as some form of hyper-efficient, serial computers could help us in thinking about the more fundamental aspects of space-time itself. Black holes as the most exotic and yet simplest forms of gravitational systems also embody quantum fluctuations that could be manipulated to archive hypercomputation, and even if this approach might not be realistic, yet it is important since it has deep connections with various aspects of quantum gravity, the highly desired unification of quantum mechanics and general relativity. The article describes how thinking about black holes as the most efficient kind of computers in the physical universe also paves the way for developing new ideas about such issues as black hole information paradox, the possibility of emulating the properties of curved space-time with the collective quantum behaviors of certain kind of condensate fluids, ideas of holographic spacetime, gravitational thermodynamics and entropic gravity, the role of quantum entanglements and non-locality in the construction of spacetime, spacetime geometry and the nature of gravitation and dark energy and dark matter, etc. to name a few.

Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological Θ-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological Θ-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.