The Ryu-Takayanagi conjecture provides a holographic description for the entanglement entropy for the strongly coupled holographic CFTs in the semi-classical limit. It proposes that the entanglement entropy is given by the area of the minimal homologous surface in the dual bulk. We show that the common terms of the entanglement entropy for the free massless fermions or bosons on a torus in the high-temperature expansion can be described by the sum of the signed area of extremal surfaces in the BTZ spacetime. The resulting EE and the corresponding bunch of the exgremal surfaces have preferable properties rather than those from the Ryu-Takayanagi conjecture.
Holographic Renormalization Group (RG) in nine dimensions is considered. The d8 holographic conformal anomaly is found. It should correspond to d8 CFT in AdS_9/CFT_8 correspondence. The comparison of holographic and QFT anomalies in d8 de Sitter space is done. It may give the indication for rigorous AdS_9/CFT_8 correspondence proposal.
The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent $c$-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support for dS/CFT correspondence. From holographic RG flow equations we calculate the holographic 4d conformal anomaly with dilatonic contributions. This conformal anomaly turns out to be the same as in AdS/CF…
We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature ($1+1$)-dimensional holographic conformal field the…
Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to …
We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to compute the holographic entanglement negativity for such mixed states i…
In this Letter, we consider a Non-Commutative (NC) extension of AdS-CFT correspondence and its effects on holographic superconductors. NC corrections are incorporated via the NC generalization of Schwarzschild black hole metric in AdS with the probe limit. We study NC effects on the relations connecting the charge density and the critical temperature of the Holographic Superconductors. Furthermore, condensation operator of the superconductor has been analyzed. Our results suggest that generically, NC effects increase the critical temperature of the holographic superconductor.
We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) dual to bulk non static $AdS_3$ geometries. Application of our proposal to such mixed states in a $CFT_{1+1}$ dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a $CFT_{1+1}$ dual to a bulk Vaidya-$AdS_3$ ge…
There is a renewed interest in conformal field theories (CFT) on ultrametric spaces (p-adic field and its algebraic extensions) in view of their natural adaptability in the holographic setting. We compute the contributions from the exchange interactions to the four-point correlator of the CFT using Witten diagrams with three-scalar interaction vertex. Together with the contributions from the bulk four-point interaction, the contact term, these provide a complete answer. We remark on the singularity structure in Mellin space, and argue that all these models are analogues of adS_2/CFT_1.
In this paper, we study the entanglement contour in a general excited state in the holographic 2d CFT using the partial entanglement entropy proposal. We show how thermodynamics fixes the entanglement contour relating it to the first law of entanglement. We derive the entanglement contour for a general time-dependent excited state and consider a quenched initial state in the presence of spatial boundaries as an explicit example. Finally, we comment on the coarse-graining and the complexity contour in the $AdS_3/CFT_2$.
In arXiv:1601.02634 it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS$_3$ (WAdS$_3$) with Dirichlet boundary conditions. In this paper, we consider AdS$_3$ and WAdS$_3$ with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS$_3$/WCFT and WAdS$…
Entanglement entropy obeys a 'first law', an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entangleme…
We consider holographic RG flows which interpolate between non-trivial ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the ``superpotentials'' which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic $c$-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the $c$-function in terms of the associated Jost functions. We propose…
We substantiate a covariant proposal for the holographic reflected entropy in $CFT$s dual to non-static $AdS$ geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the $AdS_3/CFT_2$ scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in $CFT_{1+1}$s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for t…
The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT which lives on the brane by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula is discussed. We show that when the time-like brane crosses the black hole horizon of dS Schwarzschild black hole, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional dS background.
We use the thermodynamics of anti-de Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is $ρ(Δ) \lesssim \exp\left(\frac{2πΔ}{d-1}\right)$ for CFT$_d$. Unlike the case of $d=2$, this bound is strong enough to rule out weakly coupled holographic theories. We generalize the bound to include spins $J_i$ and $U(1)$ charge $Q$, obtaining bounds on $ρ(Δ, J_i, Q)$ in $d=3$ through $6$. All bounds are saturated by black holes at the Hawking-Page transition and vanish beyond the corresponding BPS bound.
In this work, we study the holographic entanglement entropy of two dimensional $T\bar{T}$-deformed conformal field theory. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of New massive gravity, General minimal massive gravity, and Exotic general massive gravity. We also apply Song's prescription to obtain the entanglement entropy for deformed theories. In each cases, we find agreement between the results.
We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensi…
This paper investigates scalar perturbations in the top-down supersymmetric Janus solutions dual to conformal interfaces in the $D1/D5$ CFT, finding analytic closed-form solutions. We obtain an explicit representation of the bulk-to-bulk propagator and extract the two-point correlation function of the dual operator with itself, whose form is not fixed by symmetry alone. We give an expression involving the sum of conformal blocks associated with the bulk-defect operator product expansion and briefly discuss finite-temperature extensions. To our knowledge, this is the first two-point function co…
We establish our recently proposed holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with concrete higher dimensional examples. In this context we compute the holographic entanglement negativity for mixed states of adjacent subsystems in $d$-dimensional conformal field theories dual to bulk $AdS_{d+1}$ vacuum and $AdS_{d+1}$-Schwarzschild black holes. These representative examples provide strong indication for the universality of our conjecture which affirms significant implications for diverse applications.
We investigate the AdS$_3$/CFT$_2$ correspondence for the Euclidean AdS$_3$ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In both regular and $Z_N$ orbifold cases, in the sum over geometries, the two-point correlation function for massless modes factors, up to divergent terms proportional to the volume of the $SL(2,Z)/Z}$ group, into the finite sum of products of the conform…
The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for a tensor network realization of p-adic AdS/CFT, we prove that the path integral of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in the sense that the tensor network reproduces all correlation functions of the p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as axiomatized by Melzer), and can be applied not only to the p-adic plane, but also to compute any correlation functions on higher ge…
We propose a covariant holographic entanglement negativity constructionfor time-dependent mixed states of adjacent intervals in $(1+1)$-dimensional conformal field theories dual to non-static bulk $\mathrm{AdS_3}$ configurations. Our construction applied to $(1+1)$-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our conjecture to obtain the time-dependent holographic entanglement negativity for the mixed state…
In the large 't Hooft coupling limit, the hadronic size of baryon is small and nucleon-nucleon potential is obtained from massless pseudo-scalar exchanges and an infinite tower of spin one mesons exchanges. In this paper we use the holographic nucleon-nucleon interaction and obtain the corresponding potential and binding energy for deuteron and tritium nuclei. The obtained potentials are repulsive at short distances and clearly become zero by increasing distance as we expected.
The Ryu-Takayanagi conjecture predicts a holographic dual of the entanglement entropy of a CFT. It proposes that the entanglement entropy is given by the area of the minimal surface in the dual spacetime. In the semi-classical limit, this conjecture is supported by the saddle point approximation. If there are multiple classical solutions, it is assumed that only the minimal action contributes to the entanglement entropy. However, we will point out that these saddles equally contribute to the entanglement entropy in some cases. Therefore, the derivation of the conjecture is incomplete if there …
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is defined on a manifold with boundary, is one such example. Inspired by the quotienting of AdS$_3$ by spacetime isometries in order to construct multiboundary wormholes dual to multipartite CFT$_2$ states, we find that this correspondence can be understood by combining AdS/CFT with some appropriate quotient procedure. Furthermore, in three bulk dimensions, we find …
In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the $T\bar{T}$ deformation on torus in terms of perturbative CFT approach, which is the extension of the previous investigations on correlation functions defined on a plane. We systematically obtain the first order correction to the correlation functions of the CFTs with $T\bar{T}$ deformation in both operator formalism and path integral language. As a consistency check, we compute the deformed partition function, namely the zero-point correlation function, up to the first order, which is consisten…
We explicitly obtain energy-momentum tensor at the asymptotic 3-dimensional region of Schwarzschild AdS$_4$ and Taub-NUT-(A)dS$_4$ using the so-called `counter-term subtraction method' in Fefferman-Graham coordinate. The energy momentum tensor is presented in a closed form for the AdS$_4$ and for the special case of Taub-NUT-dS and in an asymptotic series for other cases. The result suggests that in light of AdS/CFT correspondence, the 3-dimensional trace anomaly can be expressed in terms of the 3-dimensional volume and Ricci scalar.
Holographic bounds have been derived using explicitly gravitational arguments. Motivated by explicit constructions of bulk wavepackets from observables in the boundary CFT, we derive a holographic bound in the context of the gauge/gravity correspondence within the dual field theory. We verify the consistency of the bound with the program of determining the Black Hole S-Matrix from the AdS/CFT correspondence.
There appears a universal logarithmic term of entanglement entropy, i.e., $-a(Ω) \log(H/δ)$, for 3d CFTs when the entangling surface has a sharp corner. $a(Ω)$ is a function of the corner opening angle and behaves as $a(Ω\to π)\simeq σ(π-Ω)^2$ and $a(Ω\to 0)\simeq κ/Ω$, respectively. Recently, it is conjectured that $σ/C_T=π^2/24 $, where $C_T$ is central charge in the stress tensor correlator, is universal for general CFTs in three dimensions. In this paper, by applying the general higher curvature gravity, we give a holographic proof of this conjecture. We also clarify some interesting probl…
We study holographic renormalization for three dimensional new massive gravity (NMG). By studying the general fall off conditions for the metric allowed by the model at infinity, we show that at the critical point where the central charges of the dual CFT are zero it contains a leading logarithmic behavior. In the context of AdS/CFT correspondence it can be identified as a source for an irrelevant operator in the dual CFT. The presence of the logarithmic fall off may be interpreted as the fact that the dual CFT would be a LCFT.
We study CFT2 conformal blocks on a torus and their holographic realization. The classical conformal blocks arising in the regime where conformal dimensions grow linearly with the large central charge are shown to be holographically dual to the geodesic networks stretched in the thermal AdS bulk space. We discuss the n-point conformal blocks and their duals, the 2-point case is elaborated in full detail. We develop various techniques to calculate both quantum and classical conformal block functions. In particular, we show that exponentiated global torus blocks reproduce classical torus blocks …
We introduce a D7-brane probe in AdS_5 x S^5 background in a way that the 4d part of the induced metric on D7-brane becomes 4d de-Sitter space (dS_4) inside AdS_5 instead of 4d Minkowski space. Although supersymmetry is completely broken, we obtain a static configuration and show the absence of dynamical tachyonic modes. Following holographic renormalization we renormalize the Dirac-Born-Infeld action of D7-brane and we completely fix the counter terms including finite contributions from the consistency under various limits. Through the AdS/CFT correspondence we study the chiral condensate and…
We use holographic methods to study the entanglement entropy for excited states in a two dimensional conformal field theory. The entangling area is a single interval and the excitations are produced by in and out vertex operators with given scaling dimensions. On the gravity side we provide the excitations by turning on a scalar field with an appropriate mass. The calculation amounts to using the gravitational background, with a singular boundary, to find the one point function of the vertex operators. The singular boundary is taken care of by introducing a nontrivial UV regulator surface to c…
We consider the expectation values of chiral primary operators in the presence of the interface in the 4 dimensional N=4 super Yang-Mills theory. This interface is derived from D3-D5 system in type IIB string theory. These expectation values are computed classically in the gauge theory side. On the other hand, this interface is a holographic dual to type IIB string theory on AdS_5 x S^5 spacetime with a probe D5-brane. The expectation values are computed by GKPW prescription in the gravity side. We find non-trivial agreement of these two results: the gauge theory side and the gravity side.
We calculate the Rényi entropy $S_q(μ,λ)$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings $λ$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\frac{\partial}{\partial q}\left({\frac{q - 1}{q}S_q(μ,λ)} \right) \ge 0$, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction o…
The purpose of this report is to provide a framework for defining phase transition processes in two dimensional holographic superconductors, and to illustrate how they are useful to be described by holographic entanglement entropy. We study holographic entanglement entropy in a two dimensional fully backrected model for holographic superconductors. We prove that phase transition could be observe using a discontinuty in the first order of entropy.
In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that two-dimensional and four-dimensional conformal anomalies (or corresponding central charges) have the same form as those obtained in AdS/CFT duality.
The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturate…
According to the holographic principle all information in the bulk of a space is coded at its border. We will check this statement in three situations involving the AdS/CFT correspondence. There is a well known equivalence between the Maxwell-Chern-Simons theory and the self-dual model in 3 dimensions when the parameters of both theories are related in a given way. We will show that when this relation holds the corresponding CFT's at the border are the same. Then we will study scalar fields. There are two quantum theories for the scalar field in AdS space. The usual prescription of the AdS/CFT…
Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator $J \bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its $J \bar T$ deformation. We find that the dual spacetime is still AdS$_3$, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show that when the coefficient of the chiral anomaly for $J$ vanis…
The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.
We solve Klein-Gordon equation for massless scalars on d+1 dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on d+1 dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Eucl…
Near horizon geometries have been widely studied, and have found many applications. Certain static, near horizon geometries are now understood to be bulk duals to CFTs with static scale-invariant sources under the AdS/CFT correspondence. However, static near-horizon geometries aren't just scale-invariant, they have extra `enhanced' symmetry. This means that they can only be the bulk duals for a special class of static, scale-invariant sources that share this enhanced symmetry. The purpose of this paper is to consider bulk duals for more generic static, scale-invariant sources, without this ext…
We perform holographic renormalization for probe branes in AdS_5 x S^5. We show that for four known probe D-branes wrapping an AdS_m x S^n, the counterterms needed to render the action finite are identical to those for the free, massive scalar in AdS_m plus counterterms for the renormalization of the volume of AdS_m. The four cases we consider are the probe D7, two different probe D5's and a probe D3. In the D7 case there are scheme-dependent finite counterterms that can be fixed by supersymmetry.
In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symme…
The bulk to boundary mapping for massive scalar fields is constructed, providing a de Sitter analog of the LSZ reduction formula. The set of boundary correlators thus obtained defines a potentially new class of conformal field theories based on principal series representations of the global conformal group. Conversely, we show bulk field operators in de Sitter may be reconstructed from boundary operators. While consistent at the level of the free field theory, the boundary CFT does not satisfy cluster decomposition. The resulting conformal field theory does not satisfy the basic axioms of Eucl…
We calculate, for the first time, three-point correlation functions involving "heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong coupling. In particular, we focus on the three-point functions of the dilaton modes and two "heavy" operators. The heavy states are dual to the single spin and dyonic magnon, the single spin and dyonic spike solutions or to two novel string solutions which do not have an undeformed counterpart. Our results provide the leading term of the correlators in the large $λ$ expansion and are in perfect agreement with the form of the correlator dict…
In this paper, we study the entanglement entropy in a large class of states of two-dimensional conformal field theory in the the large central charge limit. This class of states includes the states created by the insertion of a finite number of local heavy operators. By using the monodromy analysis, we obtain the leading order entanglement entropy for the general state. We show that it is exactly captured by the Ryu-Takayanagi formula, by using the Wilsonian line prescription in the Chern-Simons formulation of the AdS$_3$ gravity.
