Heavy-heavy-light-light (HHLL) correlators of pairwise identical scalars in CFTs with a large central charge in any number of dimensions admit a double scaling limit where the ratio of the heavy conformal dimension to the central charge becomes large as the separation between the light operators becomes null. In this limit the stress tensor sector of a generic HHLL correlator receives contributions from the multi stress tensor operators with any number of stress tensors, as long as their twist is not increased by index contractions. We show how one can compute this leading twist stress tensor sector when the conformal dimension of the light operators is large and the stress tensor sector approximates the thermal CFT correlator. In this regime the value of the correlator is related to the length of the spacelike geodesic which approaches the boundary of the dual asymptotically AdS spacetime at the points of light operator insertions. We provide a detailed description of the infinite volume limit. In two spacetime dimensions the HHLL Virasoro vacuum block is reproduced, while in four spacetime dimensions the result is written in terms of elliptic integrals.
We investigate the issues of holography and string interactions in the duality between SYM and the pp wave background. We argue that the Penrose diagram of the maximally supersymmetric pp-wave has a one dimensional boundary. This fact suggests that the holographic dual of the pp-wave can be described by a quantum mechanical system. We believe this quantum mechanical system should be formulated as a matrix model. From the SYM point of view this matrix model is built out of the lowest lying KK modes of the SYM theory on an $S^3$ compactification, and it relates to a wave which has been compactif…
We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions correspon…
We consider Lorentzian correlation functions in theories with non-relativistic Schrodinger symmetry. We employ the method developed by Skenderis and van Rees in which the contour in complex time defining a given correlation function is associated holographically with the gluing together of Euclidean and Lorentzian patches of spacetimes. This formalism extends appropriately to geometries with Schrodinger isometry.
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT$_2$. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for four-dimensional case where there is no Chern-Simons formulation for the bulk theory.
Four-dimensional (4D) flat Minkowski space admits a foliation by hyperbolic slices. Euclidean AdS3 slices fill the past and future lightcones of the origin, while dS3 slices fill the region outside the lightcone. The resulting link between 4D asymptotically flat quantum gravity and AdS3/CFT2 is explored in this paper. The 4D superrotations in the extended BMS4 group are found to act as the familiar conformal transformations on the 3D hyperbolic slices, mapping each slice to itself. The associated 4D superrotation charge is constructed in the covariant phase space formalism. The soft part gives…
We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson-Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed …
Higher-point functions of scalar operators are a rich observable in CFTs, as they contain OPE data involving multiple spinning operators. We derive the lightcone blocks for five- and six-point functions in the snowflake channel and use them to bootstrap these correlators in the lightcone limit. As a result we determine the large spin expansion of OPE coefficients involving two or three spinning operators. We verify our results by comparing to the block decomposition of higher-point functions in generalized free theory and in theories with a cubic coupling.
We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the \textit{form factor integrand}, starting from 6d holomorphic theories on twistor space. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) OPE coefficients of a 4d non-unitary CFT. We prove that conformal blocks of the chiral algebras are in one-to-one correspondence with local ope…
We study probe scalar correlation functions in a Solodukhin wormhole corresponding to the non-rotating BTZ black hole, as a toy model for microstate geometries thereof. Using real-time holography, we obtain the retarded scalar correlator in the wormhole geometry and quantitatively compare it to the result of the hybrid WKB method for the same correlator. We also calculate an off-diagonal correlator $\sim\langle H L L H' \rangle$ involving two different (heavy) wormhole states.
Motivated by the close connection of tensor models to the SYK model, we use representation theory to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge invariant operators in the free theory are computed exactly. The gauge invariant operators close a ring. The structure constants of the ring are described explicitly. Finally, we construct a collective field theory description of the bosonic tensor model.
In strongly coupled conformal field theories with a large central charge important light degrees of freedom are the stress tensor and its composites, multi-stress tensors. We consider the OPE expansion of two-point functions of the stress tensor in thermal and heavy states and focus on the contributions from the stress tensor and double-stress tensors in four spacetime dimensions. We compare the results to the holographic finite temperature two-point functions and read off conformal data beyond the leading order in the large central charge expansion. In particular, we compute corrections to th…
Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for…
As a continuation of our previous works studying the holographic principle in the plane-wave limit, we discuss the 3-point correlation functions of BMN operators with bosonic excitations when impurities are not conserved. We show that our proposal for a holographic mapping between the conformal OPE coefficients of super Yang-Mills theory and the 3-point vertex of the holographic string field theory is valid to the leading order in the large $μ$ limit. Our results provide for the first time a direct holographic relation for the 3-point correlators of BMN operators including impurity non-preserv…
We study the correlators of the 2d W_N minimal model in the semiclassical regime with large central charge from bulk viewpoint by utilizing open Wilson lines in sl(N) Chern-Simons gauge theory. We extend previous works for the tree level of bulk theory to incorporate loop corrections in this paper. We offer a way to regularize divergences associated with loop diagrams such that three point functions with two scalars and a higher spin current agree with the values fixed by the boundary W_N symmetry. With the prescription, we reproduce the conformal weight of the operator corresponding to a bulk…
We propose an explicitly calculable example of holography on 3-dimensional de Sitter space by providing a prescription to analytic continue a higher-spin holography on 3-dimensional anti-de Sitter space. Applying the de Sitter holography, we explicitly compute bulk correlation functions on 3-dimensional de Sitter space at late time in a higher-spin gravity. These expressions are consistent with recent analysis based on bulk Feynman diagrams. Our explicit computations reveal how holographic computations could provide fruitful information.
We calculate 3-point correlation functions of Delta-BMN operators with 3 scalar impurites in N=4 supersymmetric gauge theory. We use these results to test the pp-wave/SYM duality correspondence of the vertex--correlator type. This correspondence relates the coefficients of 3-point correlators of Delta-BMN operators in gauge theory to the 3-string vertex in lightcone string field theory in the pp-wave background. We verify the vertex--correlator duality equation of hep-th/0301036 at the 3 scalar impurites level for supergravity and for string modes.
We investigate the behavior of energy momentum tensor correlators in strongly coupled large-N_c Yang-Mills theory at nonzero temperature, working within the Improved Holographic QCD model. In particular, we determine the spectral functions and corresponding imaginary time correlators in the bulk and shear channels, and compare the results to recent perturbative and lattice calculations where available. For the bulk channel imaginary time correlator, for which all three results exist, lattice data is seen to favor the holographic prediction over the perturbative one over a wide range of tempera…
The holographic principle in the pp-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super Yang-Mills theory holds to the leading order in the large $μ$ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds …
Gauge theories living on stacks of D7-branes are holographically related to IIB gravitational backgrounds with a varying axion-dilaton field (F-theory). The axion-dilaton field is generated by D7, O7 and D-instanton sources and can be written in terms of the chiral correlators of the eight dimensional gauge theory living on the D7-branes. Using localization techniques, we prove that the same correlators determine the gauge coupling of the four-dimensional N=2 supersymmetric SU(2) gauge theories living on the elementary D3-brane which probes the F-theory geometries.
This is a very brief review of some results from hep-th/0112154 and hep-th/0209191. In holographic renormalization, we studied the RG flow of a 2d N=(4,4) CFT perturbed by a relevant operator, flowing to a conformal fixed point in the IR. Here, the supergravity dual is displayed, and the computation of correlators is discussed. The sample stress-energy correlator given here provides an opportunity to explicitly compare Zamolodchikov's C-function to the proposal for a "holographic C-function".
We study the correlators of two circular Wilson loops of different radii at strong coupling. In our setup one Wilson loop is located inside the other. We use holography to calculate the connected two-point function. Both an AdS background and a confining background are considered. As the computation for the confining case cannot be carried out analytically we solve the problem numerically. In the AdS case our results agree with similar holographic calculations. In the case of a confining background we find an asymptotic area law, in agreement with the result of the lattice strong coupling expa…
Celestial holography proposes a duality between the gravitational $\mathcal{S}$-matrix and correlators in a conformal field theory living on the celestial sphere. In this white paper, solicited for the 2022 Snowmass process, we review the motivation from asymptotic symmetries, fundamentals of the proposed holographic dictionary, potential applications to experiment and theory, and some important open questions.
The PP-wave/SYM proposal in its original form emphasizes a duality relation between the masses of the string states and the anomalous dimensions of the corresponding BMN operators in gauge theory, the mass--dimension type duality. In this paper, we give evidence in favour of another duality relation of the vertex--correlator type, which relates the coefficients of 3-point correlators of BMN operators in gauge theory to 3-string vertices in lightcone string field theory in the pp-wave background. We verify that all the available field theory results in the literature, as well as the newly obtai…
We consider $\mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able…
We investigate the collapse of a spherical shell of matter in an anti-de Sitter space. We search for a holographic description of the collapsing shell in the boundary theory. It turns out that in the boundary theory it is possible to find information about the radial size of the shell. The shell deforms the background spacetime, and the deformed background metric enters into the action of a generic bulk field. As a consequence, the correlators of operators coupling to the bulk field are modified. By studying the analytic structure of the correlators, we find that in the boundary theory there a…
In two spacetime dimensions the Virasoro heavy-heavy-light-light (HHLL) vacuum block in a certain limit is governed by the Catalan numbers. The equation for their generating function can be generalized to a differential equation which the logarithm of the block satisfies. We show that a similar story holds for the HHLL ${\cal W}_N$ vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the ${\cal W}_N$ blocks have the same form as the stress tensor sector of HHLL near lightcone conformal correlators in $2(N-1)$ spacetime dimensions. In the latter c…
We investigate the non-Gaussianity of primordial cosmological perturbations using holographic methods. In particular, we derive holographic formulae that relate all cosmological 3-point correlation functions, including both scalar and tensor perturbations, to stress-energy correlation functions of a holographically dual three-dimensional quantum field theory. These results apply to general single scalar inflationary universes that at late times approach either de Sitter spacetime or accelerating power-law cosmologies. We further show that in Einstein gravity all 3-point functions involving ten…
We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed $S$-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the $T\bar{T}$ deformation of the initial quantum field theory. JT gravity coupled to a single massless boson provides a promising action formulation for an integrable app…
Asymptotically AdS wormhole solutions are considered in the context of holography. Correlation functions of local operators on distinct boundaries are studied. It is found that such correlators are finite at short distances. Correlation functions of non-local operators (Wilson loops) on distinct boundaries are also studied, with similar conclusions. Deformations of the theory with multi-trace operators on distinct boundaries are considered and studied. As a consequence of these results, the dual theory is expected to factorize in the UV, and the two sectors to be coupled by a soft non-local in…
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the c…
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；University of Victoria（维多利亚大学）；Chennai Mathematical Institute（金奈数学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；The Institute of Mathematical Sciences（数学科学研究所）
In the context of higher-spin holography, we compare the classification of cubic interaction vertices for higher-spin gravity theories in three dimensions to the possible three-point correlation functions of conserved higher-spin currents in two-dimensional conformal field theories. In both cases, the allowed structures are governed by triangle inequalities for the involved spins. It is established that higher-order correlators satisfy similar polygon inequalities and that the same inequalities are valid for higher-order continuations of cubic vertices in the three-dimensional higher-spin grav…
A class of invariant states under de Sitter isometries is constructed in d-dimensional Conformal Field Theories from the universal sector of AdS/CFT dualities. These states extend the Mottola-Allen $α$-vacua to theories containing scalar primary operators of arbitrary scaling dimensions, and are proven to explicitly break conformal symmetry. Two-point correlators in these states are shown to satisfy a generalized spectral decomposition in terms of free massive propagators. It is also pointed out that the spectral decomposition of generic Euclidean correlators is known in the mathematics litera…
In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.
The generating function of correlators of dual operators on the boundary of (A)dS4 space corresponding to the conformally coupled $ϕ^4$-model is obtained up to first order in the coupling constant by using the conformal map between massless scalar fields in (Euclidean) Minkowski space and conformally coupled scalars on (Euclidean anti) de Sitter space. Some exact classical solutions of the nonlinear wave equation of massless (conformally coupled) $ϕ^3$, $ϕ^4$ and $ϕ^6$-models in D=6,4,3 Euclidean/Minkowski (AdS/dS) spaces are obtained.
Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography
INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research Jagiellonian University（雅盖隆大学理论物理研究所与马克·凯克复杂系统研究中心）；Dipartimento di Fisica e Astronomia, Università di Firenze（佛罗伦萨大学物理与天文学系）；Department of Physics and Astronomy, Ghent University（根特大学物理与天文学系）
We study correlation functions of elementary fermions in strongly interacting field theories using the AdS/CFT correspondence. This correspondence generically associates bulk fields to composite operators in field theory. We modify the holographic prescription in order to obtain correlators that correspond to fermonic single-particle excitations by introducing a dynamical fermionic source localized on a UV brane in a holographic background. We work out the conditions when these correlators obey the zeroth frequency sum-rule satisfied by angle-resolved photo-emission spectroscopy (ARPES) and ar…
We calculate holographically arbitrary n-point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.
