We propose that holographic spacetimes can be regarded as collections of quantum circuits based on path-integrals. We relate a codimension one surface in a gravity dual to a quantum circuit given by a path-integration on that surface with an appropriate UV cut off. Our proposal naturally generalizes the conjectured duality between the AdS/CFT and tensor networks. This largely strengthens the surface/state duality and also provides a holographic explanation of path-integral optimizations. For static gravity duals, our new framework provides a derivation of the holographic complexity formula given by the gravity action on the WDW patch. We also propose a new formula which relates numbers of quantum gates to surface areas, even including time-like surfaces, as a generalization of the holographic entanglement entropy formula. We argue the time component of the metric in AdS emerges from the density of unitary quantum gates in the dual CFT. Our proposal also provides a heuristic understanding how the gravitational force emerges from quantum circuits.
Holographic tensor networks associated to tilings of (1+1)-dimensional de Sitter spacetime are introduced. Basic features of these networks are discussed, compared, and contrasted with conjectured properties of quantum gravity in de Sitter spacetime. Notably, we highlight a correspondence between the quantum information capacity of the network and the cosmological constant.
Reply to "Holographic principle in spacetimes with extra spatial dimensions" and "About quantum fluctuations and holographic principle in (4+n)-dimensional spacetime"
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechani…
We do more discussions of holographic s-wave superconductors in the background of AdS3 spacetime. We analytically compute the holographic superconductor model with the motion equation has two different characteristic root on the framework of Maxwell electrodynamics field. We study superconductor models on the framework of Born-Infeld electrodynamics field and on the framework of the Stückelberg form in the background of AdS3 spacetime.
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large $N$ limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large $N$ limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse sp…
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open question. In this work, we introduce and study a map between a computational complexity measure and its holographic counterpart from first principles. We consider quantum circuits built out of conformal transformations in two-dimensional conformal field theory and a complexity measure based on assigning a cost to quantum gates via the Fubini-Study distance. We f…
We examine the five-region holographic entropy cone inequalities for the special case of the AdS$_3$-Vaidya metric for a variety of boundary configurations. This is done by numerically solving the geodesic equation in the bulk for various boundary configurations. In all the cases we examine, we find that all the inequalities are satisfied when the bulk satisfies the null energy condition, while the inequalities are all violated when the bulk spacetime violates the null energy condition. A proof of the five-region holographic entropy cone inequalities for the dynamical bulk case remains an open…
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic ent…
We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and those of another massless field living in three-dimensional null boundary $\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{μν}$ by "inverting" the bulk correlation functions and re-express the…
We consider holographic superconductors in a rotating black string spacetime. In view of the mandatory introduction of the $A_φ$ component of the vector potential we are left with three equations to be solved. Their solutions show that the effect of the rotating parameter $a$ influences the critical temperature $T_c$ and the conductivity $σ$ in a simple but not trivial way.
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 …
We examine the holographic complexity conjectures in the context of holographic theories of FRW spacetimes. Analyzing first the complexity-action conjecture for a flat FRW universe with one component, we find that the complexity grows as $t^2$, regardless of the value of $w$. In addition, we examine the holographic complexity for a flat universe sourced by a scalar field that is undergoing a transition. We find that the complexity decreases when the holographic entanglement entropy decreases for this universe. Moreover, the calculations show that, while the entanglement entropy decreases only …
We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized …
Recently we studied `vanishing' horizon limits of `boosted' black D3-brane geometry \cite{hsnr}. The type IIB solutions obtained by taking these special double limits were found to describe nonrelativistic Lifshitz spacetimes at zero temperature. In the present work we study these limits for TsT black-hole solutions which include $B$-field. The new Galilean solutions describe a holographic RG flow from Schrödinger ($a=2$) spacetime in UV to a Lifshitz universe ($a=3$) in the IR.
We investigate the evolution of the mutual information between two spatial subsystems in a compact 1+1 dimensional CFT after a quantum quench. To this end, we use the dual holographic process, given by the 2+1 dimensional Vaidya-BTZ spacetime in global coordinates, which describes the collapse of a spherically symmetric null shell. So, we first discuss the spacelike geodesic structure of this geometry and then we present the various behaviors of the holographic mutual information observed in this case. We also consider the analogous process in the adiabatic limit and compare these two cases fr…
We follow the spirit of a recent proposal to show that previous computations for asymptotically flat spacetimes in four dimensions at null infinity can be re-interpreted in terms of a well-defined holographic current algebra for the time component of the currents. The analysis is completed by the current algebra for the spatial components.
We examine holographic complexity in time-dependent Vaidya spacetimes with both the complexity$=$volume (CV) and complexity$=$action (CA) proposals. We focus on the evolution of the holographic complexity for a thin shell of null fluid, which collapses into empty AdS space and forms a (one-sided) black hole. In order to apply the CA approach, we introduce an action principle for the null fluid which sources the Vaidya geometries, and we carefully examine the contribution of the null shell to the action. Further, we find that adding a particular counterterm on the null boundaries of the Wheeler…
We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially des…
The butterfly velocity characterizes the spread of correlations in a quantum system. Recent work has provided a method of calculating the butterfly velocity of a class of boundary operators using holographic duality. Utilizing this and a presumed extension of the canonical holographic correspondence of AdS/CFT, we investigate the butterfly velocities of operators with bulk duals living in general spacetimes. We analyze some ubiquitous issues in calculating butterfly velocities using the bulk effective theory, and then extend the previously proposed method to include operators in entanglement s…
We investigate the black holes properties with a very simple and semi-classical model of spacetime discretization. In this context, we apply the Heisenberg's uncertainty principle and the equipartition energy theorem to thereto, obtaining the same thermodynamical relation of general relativity, without resorting to the Einstein field equations. This fact, show us a possible clue of convergence between general relativity and quantum physics, which we believe becomes manifest in this class of compact objects. Finally, we apply the holographic principle to thereto, introducing the concept of surf…
Under a Scherk-Schwarz compactification, the AdS soliton and black brane provide a dual description to a confinement/deconfinement phase transition. We extend this construction to asymptotically Lifshitz spacetimes. In particular, we show that there must be a phase transition between the soliton and black hole if the solutions exist. We also construct these solutions numerically and compute the phase diagram.
We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekens…
Holographic principle in spacetimes with extra spatial dimensions
F. Scardigli和R.卡萨迪奥考虑了不确定原理，其中考虑了重力的作用和可能存在的额外空间维度。他们认为，封闭在一个给定空间体积中的自由度的预测数量只与全息计数相匹配，并且没有额外的维度。考虑到额外的不确定性的距离测量，这是在他们的方法中错过了不可避免的来源，我们表明，全息特性的建议不确定原理中恢复额外的空间维度的模型。
In this second part of the study initiated in arxiv:1804.07410, we investigate holographic complexity for eternal black hole backgrounds perturbed by shock waves, with both the complexity$=$action (CA) and complexity$=$volume (CV) proposals. In particular, we consider Vaidya geometries describing a thin shell of null fluid with arbitrary energy falling in from one of the boundaries of a two-sided AdS-Schwarzschild spacetime. We demonstrate how known properties of complexity, such as the switchback effect for light shocks, as well as analogous properties for heavy ones, are imprinted in the com…
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.
We explore the cosmic evolution of a scalar field which is identified with the four dimensional spacetime volume. Given a specific form for the Lagrangian of the scalar field, a new holographic dark energy model is present. The energy density of dark energy is reversely proportional to the square of the radius of the cosmic null hypersurface which is present as a new infrared cutoff for the Universe. We find this holographic dark energy belongs to the phantom dark energy for some appropriate parameters in order to interpret the current acceleration of the Universe.
The Sturm-Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that higher the value of noncommutative parameter and Born-Infeld parameter make the condensate ha…
We present a natural generalization of holographic entanglement entropy proposals beyond the scope of AdS/CFT by anchoring extremal surfaces to holographic screens. Holographic screens are a natural extension of the AdS boundary to arbitrary spacetimes and are preferred codimension 1 surfaces from the viewpoint of the covariant entropy bound. A broad class of screens have a unique preferred foliation into codimension 2 surfaces called leaves. Our proposal is to find the areas of extremal surfaces achored to the boundaries of regions in leaves. We show that the properties of holographic screens…
We prove a c-theorem for holographic renormalization group flows in a Schrodinger spacetime that demonstrates that the effective radius L(r) monotonically decreases from the UV to the IR, where r is the bulk radial coordinate. This result assumes that the bulk matter satisfies the null energy condition, but holds regardless of the value of the critical exponent z. We also construct several numerical examples in a model where the Schrodinger background is realized by a massive vector coupled to a real scalar. The full Schrodinger group is realized when z=2, and in this case it is possible to co…
We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly non-local. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a non-local scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotic…
In this note, we describe how collections of arbitrary numbers of "BC-bits," distinct non-interacting quantum systems each consisting of a holographic boundary conformal field theory (BCFT), can be placed in multipartite entangled states in order to encode single connected bulk spacetimes that approximate geometries dual to holographic CFT states. The BC-bit version of a holographic CFT state corresponds to a geometry that can be made arbitrarily similar to the associated CFT-state geometry within a "causal diamond" region defined by points that are spacelike separated from the boundary time s…
A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by complexifying the ghost fields and flowing them in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the 1/N expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classi…
In this paper, the thermalization has been studied holographically. Explicitly in the gravity side, we consider the gravitational collapse of a thin shell of dust in a spacetime dominated by quintessence dark energy. With the thermalization probes such as the normalized geodesic length and minimal area surface, we study the effect of the state parameter for the quintessence dark energy on the thermalization. Our results show that the smaller the state parameter of quintessence is, the harder the plasma to thermalize. We also investigate the thermalization velocity and thermalization accelerati…
In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the famil…
We attempt to understand the CFT$_1$ structure underlying (2+1)D gravity in flat spacetime via dimensional reduction. We observe that under superrotation, the hyperbolic (and dS$_2$) slices of flat spacetime transform to asymptotically (A)dS$_2$ slices. We consider a wedge region bounded by two such surfaces as End-of-the-World branes and employ Wedge holography to perform holographic reduction. We show that once we consider fluctuating branes, the localised theory on the branes is Jackiw-Teitelboim (JT) theory. Finally, using the dual description of JT, we derive an 1D Schwarzian theory at th…
In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schrödinger spacetime. We consider the following setup. In the gauge theory side one can deform a given conformal field theory by a proper scalar operator and compute the quantum information metric via the two-point correlation function between two such operators. On the string side the deformation corresponds to a scalar field probing the background. In the large $N$ limit of the theory the probing can be d…
We review our recent proposal to use certain spatial cross-sections of the boundary at infinity -- light-cone cuts -- to recover the conformal metric in the bulk. We discuss some extensions of this work, including how to obtain the conformal metric near the horizon of a collapsing black hole. We also show how to obtain the conformal factor under certain conditions.
We study holographic superconductors in the Schwarzschild-AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild-AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black hole…
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theo…
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying quantum theory [2]. This `spacetime entanglement conjecture' has a holographic realization that equates the entropy formula evaluated on an arbitrary space-like co-dimension two surface with the differential entropy of a particular family of co-dimension two regions on the boundary. The differential entropy can be thought of as a directional derivative of entangle…
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some su…
The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove t…
In three spacetime dimensions, we propose a generally covariant Lorentzian action of the classicalized holographic tensor network (cHTN) as the holographic reduction of the Einstein-Hilbert action of gravity in the presence of a negative cosmological constant. In this article, first, we investigate the properties of this Lorentzian action in the ground state. Next, based on the Euclidean action of the cHTN, we derive the gravity perturbation induced by a massive particle at rest in the cHTN as the Unruh effect. Finally, we view our holographic formulation of spacetime as a non-equilibrium seco…
