We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary $CFT$.
We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix …
We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effe…
We compare the behavior of the vacuum free energy (i.e. the Casimir energy) of various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function of the spatial geometry. The CFTs we consider are a free Dirac fermion, the conformally-coupled scalar, and a holographic CFT, and we take the spatial geometry to be an axisymmetric deformation of the round sphere. The free energies of the fermion and of the scalar are computed numerically using heat kernel methods; the free energy of the holographic CFT is computed numerically from a static, asymptotically AdS dual geometry using a novel app…
We calculate all components of thermal R-current correlators from AdS/CFT correspondence for non-zero momentum and energy. In zero momentum limit, we find an analytic expression for the components Gxx(Gyy). The dielectric function of strong coupling is also presented and compared with that in weak coupling.
We consider the problem of bounding CFT correlators on the Euclidean section. By reformulating the question as an optimization problem, we construct functionals numerically which determine upper and lower bounds on correlators under several circumstances. A useful outcome of our analysis is that the gap maximization bootstrap problem can be reproduced by a numerically easier optimization problem. We find that the 3d Ising spin correlator takes the minimal possible allowed values on the Euclidean section. Turning to the maximization problem we find that for d > 2 there are gap-independent maxim…
Extending earlier results by Paulos, we discuss further the use of the embedding formalism and Mellin transform in the calculation of tree-level correlators of scalar and vector fields in AdS/CFT. We present an iterative procedure that builds amplitudes by sewing together lower-point off-shell diagrams. Both scalar and vector correlators are shown to be given in terms of Mellin amplitudes. We apply the procedure to the explicit calculation of three-, four- and five-point correlators.
We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing equation. The dispersion relations provide an equivalent formulation of the constraints of the Polyakov bootstrap and hence of crossing symmetry on the line. The built in positivity properties imply simple and exact lower and upper bounds on the values of general CFT correlators on the Euclidean section, which are saturated by generalized free fi…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to renormalized position space correlators. Several applications are presented, including the holographic boundary CFTs as well as spacelike boundary CFTs, which provide realizations of the pseudo-conformal universe.
A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS_{d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal perfectly reproduces the correct entanglement entropy in 2D CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times S^5 with that of the free N=4 super Yang-Mills.
We discuss the case of correlators in CFT made of pure contact terms, without a corresponding bare part. We show two examples. The first is provided by the conformal limits of a free massive fermion theory in 3d. We show that the (conserved) current correlators are in one-to-one correspondence with the terms of the 3d gauge CS action. The second is the Pontryagin trace anomaly. The corresponding 3-point correlator is nonvanishing even though the corresponding untraced correlator vanishes.
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of the spectrum and enjoy positivity properties at large twist. In this paper, we construct dispersive CFT functionals for correlators of unequal scalar operators in position- and Mellin-space. We then evaluate these functionals in the Regge limit to construct mixed correlator holographic CFT functionals which probe scalar particle scattering in Anti-de Sitter s…
We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts - called homogeneous and non-homogeneous - we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in $dS_4$. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators i…
We study real-time correlators in the Kerr/CFT correspondence. The near-horizon geometry of extreme and near-extremal Kerr black holes can be taken as warped spacetimes with the warping factors depending on the transverse radius and the angular variable. By considering the Kerr/CFT correspondence as a generalized warped AdS/CFT correspondence, we show how to compute the CFT real-time correlation functions. We find that the retarded Green's functions, the cross sections and the quasi-normal modes are all in perfect match with the predictions of the dual CFT. The same analysis is also generalize…
The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific…
We extend to chiral N=4 operators the holographic agreement recently found between correlators of the symmetric orbifold of M^4 at large N and type IIB strings propagating in AdS(3) x S^3 x M^4, where M^4=T^4 or K3. We also present expressions for some bulk correlators not yet computed in the boundary.
We systematically study correlators of a generic conformal field theory with a global O(2) symmetry in a sector of large global charge. We focus in particular on three- and four-point correlators with conserved current insertions sandwiched between spinful excited states corresponding to phonons over the large-charge vacuum. We also discuss loop corrections to the scaling dimensions and observe multiple logarithms in even dimensions.
We point out that an infinite class of Witten diagrams is invariant under a Yangian symmetry. These diagrams are building blocks of holographic correlators and are related by a web of differential recursion relations. We show that Yangian invariance is equivalent to the consistency conditions of the recursion relations.
We consider gravitational collapse of a massless scalar field in asymptotically Anti de Sitter spacetime. Following the AdS/CFT dictionary we further study correlations in the field theory side by way of the Klein-Gordon equation of a probe scalar field in the collapsing background. We present evidence that in a certain regime the probe scalar field behaves chaotically, thus supporting Hawking's argument in the black hole information paradox proposing that although the information can be retrieved in principle, deterministic chaos impairs, in practice, the process of unitary extraction of info…
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.
We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.
We study finite temperature effects in two distinct holographic models that exhibit Lifshitz scaling, looking to identify model independent features in the dual strong coupling physics. We consider the thermodynamics of black branes and find different low-temperature behavior of the specific heat. Deformation away from criticality leads to non-trivial temperature dependence of correlation functions and we study how the characteristic length scale in the two point function of scalar operators varies as a function of temperature and deformation parameters.
We present a short review of hep-th/0306170. In the context of AdS/CFT correspondence, we explore what information from behind the horizon of the bulk black hole geometry can be found in boundary CFT correlators. In particular, we argue that the CFT correlators contain distinct, albeit subtle, signals of the black hole singularity.
We derive the four-point correlators of scalar operators of dimension one in the supergravity limit of the D1D5 CFT holographically dual to string theory on AdS$_3\times S^3\times \mathcal{M}$, with $\mathcal{M}$ either $T^4$ or $K3$. We avoid the use of Witten diagrams but deduce our result from a limit of the heavy-heavy-light-light correlators computed in arXiv:1705.09250, together with several consistency requirements of the OPE in the various channels. This result represents the first holographic correlators of single-trace operators computed in AdS$_3$.
N-point correlation functions of conserved currents and weight-two scalar operators of the three-dimensional free fermion vector model are found as invariants of the higher-spin symmetry in four-dimensional AdS. These are the correlators of the unbroken Vasiliev higher-spin theory. The results extend the recent work arXiv:1210.7963 and are complementary to arXiv:1301.3123 where the correlators were computed entirely on the boundary.
We show that next-to-extremal correlators of chiral primary operators in N=4 SYM theory do not receive quantum corrections to first order in perturbation theory. Furthermore we consider next-to-extremal correlators within AdS supergravity. Here the exchange diagrams contributing to these correlators yield results of the same free-field form as obtained within field theory. This suggests that quantum corrections vanish at strong coupling as well.
We show that the scaling dimensions of lowest operators in conformal field theories (CFTs) can be isolated in small and closed regions from single correlator bootstrap. We find the conserved currents play crucial roles in bootstrapping the crossing equation. By imposing a mild gap between the scaling dimensions of the conserved current and its next operator, the scaling dimensions of lowest operators are forced to lie in small isolated regions, i.e., these CFTs can be almost fixed by few lowest operators in certain channels. For CFTs with extended supersymmetry, the single correlator crossing …
The AdS/CFT correspondence predicts a phase transition in Wilson loop correlators in the strong coupling N=4, D=4 SYM theory which arises due to instability of the classical string stretched between the loops. We study this transition in detail by solving equations of motion for the string in the particular case of two circular Wilson loops. The transition is argued to be smoothened at finite `t Hooft coupling by fluctuations of the string world sheet and to be promoted to a sharp crossover. Some general comments about Wilson loop correlators in gauge theories are made.
We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.
We study the two circular Wilson loop correlator in which one is of anti-symmetric representation, while the other is of fundamental representation in 4-dimensional ${\cal N}=4$ super Yang-Mills theory. This correlator has a good AdS dual, which is a system of a D5-brane and a fundamental string. We calculated the on-shell action of the string, and clarified the Gross-Ooguri transition in this correlator. Some limiting cases are also examined.
We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the reno…
Two-dimensional conformal field theories at large central charge and with a sufficiently sparse spectrum of light states have been shown to exhibit universal thermodynamics. This thermodynamics matches that of AdS$_3$ gravity, with a Hawking-Page transition between thermal AdS and the BTZ black hole. We extend these results to correlation functions of light operators. Upon making some additional assumptions, such as large $c$ factorization of correlators, we establish that the thermal AdS and BTZ solutions emerge as the universal backgrounds for the computation of correlators. In particular, W…
Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1,2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formall…
By solving the equations of motion of massive $p$-form potential in Anti-de-Sitter space and using the $AdS/CFT$ correspondence of Maldacena, the generating functional of two-point correlation functions of the currents is obtained. When the mass parameter vanishes the result agrees with the known massless case.
We find a covariant expression for the universal part of the holographic entanglement entropy which is valid for CFTs dual to generic higher curvature gravities in up to five bulk dimensions. We use this functional to compute universal coefficients of stress-tensor correlators in three-dimensional CFTs dual to Cubic Curvature Gravity. Using gauge/gravity duality, we work out an expression for the entanglement entropy of deformed entangling regions and read the coefficients from the power expansion of the entropy in the deformation parameter. In particular, we obtain the $t_4$ coefficient of th…
We continue our study of string correlators on Euclidean $\text{AdS}_3$ with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show that correlators exhibit a simple behaviour near their singularities. The spacetime correlators are meromorphic functions in the $\mathrm{SL}(2,\mathbb{R})$-spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual $\text{CFT}_2$. Moreover, we also compute the residues of the spacetime correlators for some of the poles …
We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group, and generalize the Lunin-Mathur covering space technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. We work two examples, one using a simple bosonic CFT, and one using the …
This note is aimed at presenting a new algebraic approach to momentum-space correlators in conformal field theory. As an illustration we present a new Lie-algebraic method to compute frequency-space two-point functions for charged scalar operators of CFT$_{1}$ dual to AdS$_{2}$ black hole with constant background electric field. Our method is based on the real-time prescription of AdS/CFT correspondence, Euclideanization of AdS$_{2}$ black hole and projective unitary representations of the Lie algebra $\mathfrak{sl}(2,\mathbb{R}) \oplus \mathfrak{sl}(2,\mathbb{R})$. We derive novel recurrence …
Recently exact agreement has been found between three-point correlators of chiral operators computed in string theory on AdS_3 x S^3 x T^4 with NS-NS flux and those computed in the symmetric orbifold CFT. However, it has also been shown that these correlators disagree with those computed in supergravity, under any identification of single particle operators which respects the symmetries. In this note we resolve this disagreement: the key point is that mixings with multi-particle operators are not suppressed even at large N in extremal correlators. Allowing for such mixings, orbifold/string the…
We consider current-current correlators in 4d $\N =1$ SCFTs, and also 3d $\N =2$ SCFTs, in connection with AdS/CFT geometry. The superconformal $U(1)_R$ symmetry of the SCFT has the distinguishing property that, among all possibilities, it minimizes the coefficient, $τ_{RR}$ of its two-point function. We show that the geometric Z-minimization condition of Martelli, Sparks, and Yau precisely implements $τ_{RR}$ minimization. This gives a physical proof that Z-minimization in geometry indeed correctly determines the superconformal R-charges of the field theory dual. We further discuss and compar…
In this note we study the symmetry-breaking phases of 3D gravity coupled to matter. In particular, we consider black holes with scalar hair as a model of symmetry-breaking phases of a strongly coupled 1+1 dimensional CFT. In the case of a discrete symmetry, we show that these theories admit metastable phases of broken symmetry and study the thermodynamics of these phases. We also demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry breaking at low temperature. The apparent contradiction with the Coleman-Mermin-Wagner theorem is discussed.
In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering of Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=12J$ and temperatures $T_L=\frac{(r_++r_-)-Q^2/M}{4πa}, T_R=\frac{r_+-r_-}{4πa}$. Using the Minkowski prescription, we compute the real-time correlators o…
A previous calculation of the phase transition in the Wilson loop correlator in the zero temperature AdS/CFT correspondence is extended to the case where the loops are concentric circles of unequal radii. This phase transition occurs due to the instability of the classical string stretched between the loops. We compute the string action and its expansion in the distance h between the loops for small h. We also find that the connected minimal surface is subleading or does not even exist when h=0 and the radii are considerably different. This feature has no analogue in flat space.
We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields dual to operators ${\cal O}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $AdS_5 \times S^5$ three-point function in the literature. For such extremal correlators we find perfect agreement with the conformal field theory side, provided that the coupling of the cubic interaction contains a vanishing…
In this work, we study the $\frac{1}{8}$-BPS heavy-heavy-light-light correlators in the D1D5 CFT and its holographic dual. On the field theory side, we compute the fermionic four-point correlators at the free orbifold point. On the dual gravity side, we compute the correlators of the scalar operators in the supergravity limit of the D1D5 CFT. Following the strategy of \cite{Galliani:2017jlg}, the four-point function is converted into a two-point function in non-trivial geometries known as superstrata which are supergravity solutions preserving $1/8$ supersymmetries. We focus on a family of int…
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…
The BPS correlators of the symmetric product orbifold $\text{Sym}_N(\mathbb{T}^4)$ are reproduced from the dual worldsheet theory describing strings on $\text{AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with minimal ($k=1$) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet.
We use large spin perturbation theory and the Lorentzian inversion formula to compute order-$\varepsilon$ corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT in $4 - \varepsilon$ dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving $φ$ and $φ^2$, for $φ^2$ in both the singlet and symmetric traceless representations of $O(n)$. We extend some computations to the next order, and find order-$\varepsilon^2$ data for a number of quantities for the Ising case at $n = 1$. Along the way, we discuss several interestin…
