It has been suggested that a $dS_{d+1}$ spacetime of radius $R_{ds}$ has a holographic dual, living at future space-like infinity ${\cal I}^+$, with the bulk wave function being dual to the partition function of the boundary theory, [arXiv:astro-ph/0210603v5]. We consider some aspects of this correspondence. For under damped scalars with mass $M^2R_{ds}^2>{d^2\over4}$, belonging to the principal series, we show that for the Bunch Davies vacuum a suitable source in the boundary theory can be identified in terms of the coherent state representation of the wave function. We argue that terms in the resulting correlation functions, which are independent of the late time cut-off, satisfy the Ward identities of a conformal field theory. We also discuss other ways to identify sources, both in the under damped and the over damped case, where $M^2R_{ds}^2<{d^2\over4}$, and argue that these too can lead to correlators satisfying the Ward identities of a CFT. Some comments on the violation of reflection positivity, and the cut-off dependent terms, along with some explicit checks and sample calculations, are also included.
Recently, a codimension two holography called wedge holography is proposed as a generalization of AdS/CFT. It is conjectured that a gravitational theory in $d+1$ dimensional wedge spacetime is dual to a $d-1$ dimensional CFT on the corner of the wedge. In this paper, we give an exact construction of the gravitational solutions for wedge holography from the ones in AdS/CFT. By applying this construction, we prove the equivalence between wedge holography and AdS/CFT for vacuum Einstein gravity, by showing that the classical gravitational action and thus the CFT partition function in large N limi…
We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography can be obtained by taking the zero-volume limit of holographic defect CFT. Remarkably, it can be regarded as a holographic dual of the edge modes on the defects. For one class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the …
We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimensional because the interactions do not propagate in one of the dimensions. The D-dimensional action for the field theory can be identified with the sum over (D-1)-dimensional actions with all possible values $Λ$ of the UV cutoff, so that the extra hidden dimension can be identified with $Λ$. Since there are no interactions in the extra dimension, m…
Using the AdS/CFT correspondence we study the holographic principle and the CFT/FRW relations in the near-horizon AdS(5)xS(5) geometry with a probe D3-brane playing the role of the boundary to this space. The motion of the probe D3-brane in the bulk, induces a cosmological evolution on the brane. As the brane crosses the horizon of the bulk black hole, it probes the holography of the dual CFT. We test the holographic principle and we find corrections to CFT/FRW relations in various physical cases: for radially moving, spinning and electrically charged D3-brane and for a NS/NS B-field in the bu…
By studying global AdS using different foliations, global and Rindler-AdS, we show that there are two different asymptotic Fefferman-Graham expansions possible and thus two different definitions of "boundaries". We demonstrate that imposing boundary conditions on the two boundaries is not mutually compatible even when these boundaries are pushed to infinity. Thus, these two procedures define two genuinely distinct theories that we call global-CFT and Rindler-CFT. We show that the Rindler-CFT is not the same as the theory one gets by "Rindlerizing the global-CFT" as described in hep-th/9804085.…
The principle of the holography of information states that in a theory of quantum gravity a copy of all the information available on a Cauchy slice is also available near the boundary of the Cauchy slice. This redundancy in the theory is already present at low energy. In the context of the AdS/CFT correspondence, this principle can be translated into a statement about the dual conformal field theory. We carry out this translation and demonstrate that the principle of the holography of information holds in bilocal holography.
It is shown that the correspondence principle and the holographic principle are incompatible in the background of an eternal Schwarzschild-anti-de Sitter geometry. The argument is based on the observation that algebraic structures of local quantum field and CFT operators are not equivalent. This implies, in particular, the bulk CFT must be singular near the black-hole horizon. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory.
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校曼尼·L·巴乌米克理论物理研究所物理学与天文学系）
In this thesis we give explicit results for bosonic string amplitudes on AdS_3 x S^3 and the corresponding plane-wave limit. We also analyze the consequences of our approach for understanding holography in this set up, as well as its possible generalization to other models.
We investigate a new approach to holography in asymptotically AdS spacetimes, in which time rather than space is the emergent dimension. By making a sufficiently large T^2-deformation of a Euclidean CFT, we define a holographic theory that lives on Cauchy slices of the Lorentzian bulk. (More generally, for an arbitrary Hamiltonian constraint equation that closes, we show how to obtain it by an irrelevant deformation from a CFT with suitable anomalies.) The partition function of this theory defines a natural map between the bulk canonical quantum gravity theory Hilbert space, and the Hilbert sp…
In this paper it is shown how the AdS/CFT correspondence extends to a more general situation in which the first theory is defined on (d+1)-dimensional manifold $\tilde M$ defined as the filling in of a compact d-dimensional manifold M. The stability of the spectral correspondence mass/conformal-weight under such geometry changes is also proven.
The holographic principle asserts that the complete description of the interior of a sphere is a theory which not only lives on the surface of the sphere, but also has A/4 binary degrees of freedom. In this context we revisit the question of whether AdS/CFT is fully holographic. We construct states which are localized deep in the interior yet are encoded on short scales in the CFT, seemingly in conflict with the UV/IR prescription. We make a proposal to address the more basic question of which CFT states are sufficient to describe physics within a certain region of the bulk.
The Ryu-Takayanagi (RT) formula has been a key ingredient in our understanding of holography. Recent work on TT deformations has also boosted our understanding of holography away from the conformal boundary of AdS. In this short note, we aim to refine some recent work demonstrating the success of the RT formula in TT deformed theories. We emphasize general arguments that justify the use of the RT formula in general holographic theories that obey a GKPW-like dictionary. In doing so, we clarify subtleties related to holographic counterterms and discuss the implications for holography in general …
Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as "superstrata" provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point funct…
Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. …
We interpret the traversable wormhole in AdS/CFT in the context of quantum information theory. In particular, we investigate its properties as both a quantum channel and entanglement witness. We define protocols that allow either the bounding of the channel's entanglement capacity or the determination of aspects of the entanglement structure between the two boundary CFTs. Such protocols and connections allow for the use of quantum channel techniques in the study of gravitational physics and vice versa. More generally, our results suggest a purely quantum information-theoretic criterion for rec…
We explore some aspects of holographic dual of Boundary Conformal Field Theory (BCFT). In particular we study asymptotic symmetry of geometries which provide holographic dual of BCFTs. We also compute two-point functions of certain bosonic and fermionic operators in the dual BCFT by making use of AdS/BCFT correspondence.
A few supergravity solutions representing configurations of NS5-branes admit exact conformal field theory (CFT) description. Deformations of these solutions should be described by exactly marginal operators of the corresponding theories. We briefly review the essentials of these constructions and present, as a new case, the operators responsible for turning on angular momentum.
We briefly review the AdS3/CFT2 correspondence and the holographic issues that arise in the Penrose limit. Exploiting current algebra techniques, developped by D'Appollonio and Kiritsis for the closely related Nappi-Witten model, we obtain preliminary results for bosonic string amplitudes in the resulting Hpp-wave background and comment on how to extend them to the superstring.
We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations'. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/C…
We give a simple nonsupersymmetric example in which chronology protection follows from unitarity and the AdS/CFT correspondence. We consider a ball of homogeneous, rotating dust in global AdS3 whose backreaction produces a region of Goedel space inside the ball. We solve the Israel matching conditions to find the geometry outside of the dust ball and compute its quantum numbers in the dual CFT. When the radius of the dust ball exceeds a certain critical value, the spacetime will contain closed timelike curves. Our main observation is that precisely when this critical radius is exceeded, a unit…
We show by means of the AdS/CFT correspondence in the context of quantum gravity how inter-representational relations - loosely speaking relations among different equivalent representations of one and the same physics - can play out as a tool for intra-theoretical developments and thus boost theory development in the context of discovery. More precisely, we first show that, as a duality, the AdS/CFT correspondence cannot in itself testify to the quantum origin of gravity (though it may be utilized for this purpose). We then establish through two case studies from emergent gravity (Jacobson (20…
Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT,…
The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension $D$. For CFT's with a large number of fields, $N$, the CEB is found to be valid for temperatures not exceeding a value of order $M_P/N^{1\over D-2}$, in agreement with large $N$ bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFT's and strongly coupled CFT's with AdS duals, the CEB, despite the fac…
We show that the existent fuzzy S^2 and S^4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS_2 X S^2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzzy AdS_2 model whose fundamental commutation relation may underlie the UV/IR connection.
We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity ($d=3$), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reprod…
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Universitat de Barcelona（巴塞罗那大学）；Inamori Research Institute for Science（稻盛科学研究所）
Inspired by the general relation between the boundary global symmetry and the bulk gauge symmetry in AdS/CFT, we reformulate the $d+1$ dimensional AdS gravity theory as a $SO(2,d)$ gauge theory. In this formalism, the pull back of the bulk equation of motion onto a co-dimension one hypersurface $Σ$ can be naturally related to the $SO(2,d)$ conservation law under a local energy scale in the dual CFT. The consistency of CFT requires that the $SO(2,d)$ covariant anomaly vanishes at arbitrary scale. After imposing a covariant area law as the renormalization condition, the vanishing of $SO(2,d)$ an…
We consider the non-local operator ${\mathcal T}$ defined in 2-dimensional CFTs by the path integral over a torus with two punctures. Using the AdS/CFT correspondence, we study the spectrum and ground state of this operator in holographic such CFTs in the limit of large central charge $c$. In one region of moduli space, we argue that the operator retains a finite gap and has a ground state that differs from the CFT vacuum only by order one corrections. In this region the torus operator is much like the cylinder operator. But in another region of moduli space we find a puzzle. Although our ${\m…
Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional quantum theory of gravity and low dimensional theory possible. Detail counting for observable degrees of freedom of quantum system of gravity in the bulk of noncommutative space SO_q(3) and the classical limit of its boundary surface S^2 is discussed. Taking noncommutivity effect into account, we get the desired form of entropy for our world, which is consistent…
The issue of holographic mapping between bulk and boundary in the plane-wave limit of AdS/SYM correspondence is reexamined from the viewpoint of correlation functions. We first study the limit of large angular momentum for the so-called GKP-W relation in supergeravity approximation, connecting directly the effective action in the bulk and the generating functional of correlation functions on the boundary. The spacetime tunneling picture which has been proposed in our previous works naturally emerges. This gives not only a justification of our previous proposal, with some important refinements,…
We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the k…
The issue of holographic principle in the PP-wave limit of the AdS/CFT correspondence is discussed, in the hope of clarifying some confusions in the literature. We show that, in the plane-wave limit, the relation between the partition function in the bulk and the gauge-invariant correlation functions on the boundary should be interpreted on the basis of a tunneling picture in the semi-classical approximation which is appropriate for the plane-wave limit. This leads to a natural relation between Euclidean S-matrix in the bulk and the short-distance operator-product expansion of the so-called BM…
Given an asymptotically Anti-de Sitter supergravity solution, one can obtain a microscopic interpretation by identifying the corresponding state in the holographically dual conformal field theory. This is of particular importance for heavy pure states that are candidate black hole microstates. Expectation values of light operators in such heavy CFT states are encoded in the asymptotic expansion of the dual bulk configuration. In the D1-D5 system, large families of heavy pure CFT states have been proposed to be holographically dual to smooth horizonless supergravity solutions. We derive the pre…
Time-dependent entanglement entropy (EE) is computed for a single interval in two-dimensional conformal theories from a quenched initial state in the presence of spatial boundaries. The EE is found to be periodic in time with periodicity equal to the system size $L$. For large enough $L$, the EE shows a rise to a thermal value (characterized by a temperature $1/β$ determined by the initial state), followed by periodic returns to the original value. This works irrespective of whether the conformal field theory (CFT) is rational or irrational. For conformal field theories with a holographic dual…
According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived concept: points are obtained by considering the incidence of twistors. One needs two twistors to obtain a point. Twistor is thus a ``square root'' of a point. In the present paper we entertain the idea of quantizing the space of twistors. Twistors, and thus also spacetime points become operators acting in a certain Hilbert space. The algebra of functions on spac…
A duality between the large N 't Hooft limit of the WD_N minimal model CFTs and a higher spin gravity theory on AdS3 is proposed. The gravity theory has massless spin fields of all even spins s=2,4,6,..., as well as two real scalar fields whose mass is determined by the 't Hooft parameter of the CFT. We show that, to leading order in the large N limit, the 1-loop partition function of the higher spin theory matches precisely with the CFT partition function.
We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At $n$-points, the QF…
We generalize the $T\overline{T}$ deformation of CFT$_2$ to higher-dimensional large-$N$ CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables.
We analyze the $δ=2$ Tomimatsu-Sato spacetime in the context of the proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is asymptotically flat and has a well-defined ADM mass and angular momentum, but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a region with closed timelike curves and a rod-like conical singularity. We demonstrate that the near horizon geometry belongs to a general class of Ricci-flat metrics with $SL(2,\mathbb{R})\times U(1)$ symmetry that includes both the extremal Kerr and extrema…
The locality of bulk physics at distances below the AdS length is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a planar expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjectu…
These notes were prepared for the introductory lectures on Higher Spin Holography presented at the Twelfth Modave Summer School in Mathematical Physics 2016, aimed at Ph.D. students and researchers new to this topic. Contents: 1. Higher spin particles in AdS 2. The AdS/CFT correspondence and higher spins 3. The ambient space formalism 4. Witten diagrams for higher spin fields / higher spin interactions from CFT
We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. Howev…
We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitud…
