We study stress-tensor correlators in the $T\bar{T}$-deformed conformal field theories in two dimensions. Using the random geometry approach to the $T\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $T\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\bar{T}$ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $T\bar{T}$-deformed operator product expansions of the stress tensor. A salient feature of the $T\bar{T}$-deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.
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…
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 …
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.
An important part of a CFT four-point function, the stress tensor sector, comprises the exchanges of the stress tensor and its composites. The OPE coefficients of these multi-stress tensor operators and consequently, the complete stress tensor sector of four-point functions in CFTs with a large central charge, can be determined by computing a heavy-heavy-light-light correlator. We show how one can make substantial progress in this direction by bootstrapping a certain ansatz for the stress tensor sector of the correlator, iteratively computing the OPE coefficients of multi-stress tensor operato…
The evaluation of field theoretic correlators at strong couplings is especially interesting in the light of recently discovered string/field theory correspondences. We present a calculation of the stress-tensor correlator in N=1 SYM theory in 2+1 dimensions. We calculate this object numerically with the method of supersymmetric discrete light-cone quantization (SDLCQ) at large N_c. For small distances we reproduce the conformal field theory result with the correlator behaving like 1/r^6. In the large r limit the correlator is determined by the (massless) BPS states of the theory. We find a cri…
The large $N$ limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an $\mathfrak{sl}(2,\mathbb{R})$ WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.
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 …
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.
We compute the superconformal partial waves of the four-point correlator $\langle JJJJ\rangle$, in which the external operator $J$ is the superconformal primary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In $\mathcal{N}=2$ SCFTs, the three-point functions $\langle \mathcal{J}\mathcal{J}\mathcal{O}\rangle$ with general multiplet $\mathcal{O}$ contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be ni…
We consider free superconformal theories of n=8 scalar multiplet in d=3 and (2,0) tensor multiplet in d=6 and compute 2-point and 3-point correlators of their stress tensors. The results for the 2-point and 3-point correlators for a single d=3 and d=6 multiplet differ from the "strong-coupling" AdS_4 and AdS_7 supergravity predictions by the factors $4\sqrt2 \over 3π}N^{3/2}$ and $4N^3$ respectively. These are the same factors as found earlier in hep-th/9703040 in the comparison of the brane free field theory and the 11-d supergravity predictions for the absorption cross-sections of longitudin…
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…
We express stress tensor correlators using the Schwinger-Keldysh formalism. The absence of off-diagonal counterterms in this formalism ensures that the +- and -+ correlators are free of primitive divergences. We use dimensional regularization in position space to explicitly check this at one loop order for a massless scalar on a flat space background. We use the same procedure to show that the ++ correlator contains the divergences first computed by `t Hooft and Veltman for the scalar contribution to the graviton self-energy.
The stress tensor sector of a heavy-heavy-light-light scalar correlator in CFTs with a large central charge and a large gap is defined by the exchange of multi-stress tensor operators. The Regge limit of this correlator is determined by the phase shift of a highly energetic particle propagating in a dual black hole background. Assuming Einstein gravity in the bulk, the phase shift is known perturbatively to all orders in the ratio of the heavy scaling dimension over the central charge. In the CFT, the order counts the number of stress tensors in the multi-stress tensor operator. By Fourier tra…
We study second order relativistic viscous hydrodynamics in 4-dimensional conformal field theories. We derive Kubo-type relations for second order hydrodynamic coefficients in terms of 3-point stress tensor retarded correlators. For N=4 super Yang-Mills theory at strong coupling and at finite temperature we compute these stress tensor 3-point correlators, using AdS/CFT, by evaluating real-time cubic Witten diagrams in the AdS-Schwarzschild background. The small momentum expansion of the 3-point correlators in terms of first and second order hydrodynamic coefficients is matched with the AdS res…
We compute four point functions of the stress tensor and conserved currents in AdS_4/CFT_3 using bulk perturbation theory. We work at treel level in the bulk theory, which we take to be either pure gravity or Yang Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four point correlator with arbitrary external helicities and momenta. We …
Recent advances in string theory have highlighted the need for reliable numerical methods to calculate correlators at strong coupling in supersymmetric theories. We present a calculation of the correlator <0|T^{++}(r)T^{++}(0)|0> in N=1 SYM theory in 2+1 dimensions. The numerical method we use is supersymmetric discrete light-cone quantization (SDLCQ), which preserves the supersymmetry at every order of the approximation and treats fermions and bosons on the same footing. This calculation is done at large $N_c$. For small and intermediate r the correlator converges rapidly for all couplings. A…
In this paper we calculate the vacuum expectation values of the stress-energy bitensor of a massive quantum scalar field with general coupling to N-dimensional Euclidean spaces and hyperbolic spaces which are Euclidean sections of the anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1,2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because these spaces are maximally symmetric the eigenm…
We consider correlation functions of the stress-tensor or a conserved current in AdS_{d+1}/CFT_d computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree level. These relations have an advantage over the BCFW-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons …
We discuss to what extent the full set of Ward Identities constrain the four-point function of the stress-energy tensors or conserved currents in a conformal field theory. We calculate the number of kinematically unrestricted functional degrees of freedom governing the corresponding correlators and find that it matches the number of functional degrees of freedom governing scattering amplitudes of some "dual" massless particles in the auxiliary Minkowski space. We also formulate the conformal bootstrap constraints for the correlators in question in terms of only unrestricted degrees of freedom.…
Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest one-point energy correlator implies that 1/3 <= a/c <= 31/18 where a and c are the Weyl anomaly coefficients. We use the positivity of high…
We calculate the expectation values of the stress-energy bitensor defined at two different spacetime points $x, x'$ of a massless, minimally coupled scalar field with respect to a quantum state at finite temperature $T$ in a flat $N$-dimensional spacetime by means of the generalized zeta-function method. These correlators, also known as the noise kernels, give the fluctuations of energy and momentum density of a quantum field which are essential for the investigation of the physical effects of negative energy density in certain spacetimes or quantum states. They also act as the sources of the …
In this article we probe the proposed holographic duality between $T\bar{T}$ deformed two dimensional conformal field theory and the gravity theory of $\rm AdS_3$ with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $T\bar{T}$ CFT in a Euclidean plane and in a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in $\rm AdS_3$ with the corresponding cutoff surface, given a hologra…
We compute the central charge $C_T$ and universal conductivity $C_J$ of $N_F$ fermions coupled to a $U(1)$ gauge field up to next-to-leading order in the $1/N_F$ expansion. We discuss implications of these precision computations as a diagnostic for response and entanglement properties of interacting conformal field theories for strongly correlated condensed matter phases and conformal quantum electrodynamics in $2+1$ dimensions.
Semiclassical Physics in gravitational scenario, in its first approximation (1st order) cares only for the expectation value of stress energy tensor and ignores the inherent quantum fluctuations thereof. In the approach of stochastic gravity, on the other hand, these matter fluctuations are supposed to work as the source of geometry fluctuations and have the potential to render the results from 1st order semiclassical physics irrelevant. We study the object of central significance in stochastic gravity, i.e. the noise kernel, for a wide class of Friedmann space-times. Through an equivalence of…
We show that, although the correlator of four stress-tensor multiplets in N=4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a pred…
We use the twistor-string theory on the B-model of CP^{3|4} to compute the maximally helicity violating(MHV) tree amplitudes for conformal supergravitons. The correlator of a bilinear in the affine Kac-Moody current(Sugawara stress-energy tensor) can generate these amplitudes. We compare with previous results from open string version of twistor-string theory. We also compute the MHV tree amplitudes for both gravitons and gluons from the correlators between stress-energy tensor and current.
We calculate the vacuum expectation values of the stress-energy bitensor of a minimally coupled massless scalar field in anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1,2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because the AdS spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta-function [3,4]. Upon taking the seco…
We present a general procedure to renormalize the stress tensor two-point correlation function on a Minkowski background in position space. The method is shown in detail for the case of a free massive scalar field in the standard Minkowski vacuum state, and explicit expressions are given for the counterterms and finite parts, which are in full accordance with earlier results for the massless case. For the general case in position space, only regularized --- but not renormalized --- results have been obtained previously. After a Fourier transformation to momentum space, we also check agreement …
We calculate correlation functions of the R-current or the stress-energy tensor T_{μν} with two non-protected operators dual to generic massive string states with rotation in S^5, in the context of the AdS/CFT correspondence. Field theory Ward identities make predictions about the all-loop behaviour of these correlators. In particular, they restrict the fusion coefficient to be proportional to the R-charge of the operators or to their dimension, respectively, with certain coefficients of proportionality. We reproduce these predictions, at strong coupling, using string theory. Furthermore, we p…
In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator $\barΨΨ$ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator $\barΨΨ$ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the …
This paper concerns a special class of $n$-point correlation functions of operators in the stress tensor supermultiplet of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory. These are "maximal $U(1)_Y$-violating" correlators that violate the bonus $U(1)_Y$ charge by a maximum of $2(n-4)$ units. We will demonstrate that such correlators satisfy $SL(2,\mathbb{Z})$-covariant recursion relations that relate $n$-point correlators to $(n-1)$-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory.…
We consider four-point functions of operators in the stress tensor multiplet of the 3d $\mathcal{N}=6$ $U(N)_k\times U(N+M)_{-k}$ or $SO(2)_{2k}\times USp(2+2M)_{-k}$ ABJ theories in the limit where $M$ and $k$ are taken to infinity while $N$ and $λ\sim M/k$ are held fixed. In this limit, these theories have weakly broken higher spin symmetry and are holographically dual to $\mathcal{N}=6$ higher spin gravity on $AdS_4$, where $λ$ is dual to the bulk parity breaking parameter. We use the weakly broken higher spin Ward identities, superconformal Ward identities, and the Lorentzian inversion for…
We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial operators, in each case finding new features and new complications: for scalar correlators, renormalisation leads to beta functions, novel conformal anomalies of type B, and unexpected analytic structure in momentum space; for correlators of stress tensors and/or conserved currents, beta functions vanish but anomalies of both type B and type A (associated with a $…
We compute the correlation functions of 3 and 4 stress energy tensors $(T)$ in D=3 in free field theories of scalars, abelian gauge fields, and fermions, which are relevant in the analysis of cosmological non-gaussianities. These correlators appear in the holographic expressions of the scalar and tensor perturbations derived for holographic cosmological models. The result is simply adapted to describe the leading contributions in the gauge coupling to the same correlators also for a non abelian SU(N) gauge theory. In the case of the bispectrum, our results are mapped and shown to be in full ag…
We continue the study of the duality between super-correlators and scattering super-amplitudes in planar N=4 SYM. We provide a number of further examples supporting the conjectured duality relation between these two seemingly different objects. We consider the five- and six-point one-loop NMHV and the six-point tree-level NNMHV amplitudes, obtaining them from the appropriate correlators of strength tensor multiplets in N=4 SYM. In particular, we find exact agreement between the rather non-trivial parity-odd sector of the integrand of the six-point one-loop NMHV amplitude, as obtained from the …
We study the two-point function of the stress-tensor multiplet of $\mathcal{N}=4$ SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the $20'$ irrep of the $\mathfrak{so}(6)_\text{R}$ R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial. We use a combination of perturbation theory and defect CFT techniques to obtain results up to next-to-leading order in the coupling constant. Being a defect CFT correlator, there exist two (super)conformal block expans…
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other hal…
We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level ampli…
From chiral to conformal anomalies: a double copy perspective for CFT correlators
Università del Salento（萨伦托大学）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Center for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR-nanotec, Lecce（意大利国家研究委员会纳米技术研究所莱切分部）
Using holographic renormalization, we study correlation functions throughout a renormalization group flow between two-dimensional superconformal field theories. The ultraviolet theory is an N=(4,4) CFT which can be thought of as a symmetric product of U(2) super WZW models. It is perturbed by a relevant operator which preserves one-quarter supersymmetry and drives the theory to an infrared fixed point. We compute correlators of the stress-energy tensor and of the relevant operators dual to supergravity scalars. Using the former, we put together Zamolodchikov's C function, and contrast it with …
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal correlators. We proceed with our analysis in momentum space and we illustrate the theory of the conformal anomalies. We move on to analyse the renormalization of the correlators through counterterms followed by a discussion of the anomaly action. In the second part of the thesis. we derive and analyze the conformal Ward identities (CWIs) of a tensorial 4-point function…
In this note we present a simple method of constructing general conformally invariant three point functions of operators of various spins in three dimensions. Upon further imposing current conservation conditions, we find new parity violating structures for the three point functions involving either the stress-energy tensor, spin one currents, or higher spin currents. We find that all parity preserving structures for conformally invariant three point functions of higher spin conserved currents can be realized by free fields, whereas there is at most one parity violating structure for three poi…
In this short note we use the flat space limit and the relation between the 4-pt correlation function of the bottom and top components of the stress tensor multiplet to constraint its stringy corrections at strong coupling in the planar limit. Then we use this four point function to compute corrections to the anomalous dimension of double trace operators of the Lagrangian density and to compute energy-energy correlators at strong coupling.
Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by tuning the dimensionless charge density to magnetic field ratio, exhibits nontrivial scaling in its thermodynamic properties, and an associated nontrivial dynamical critical exponent. In the present work, we analytically compute low energy correlation functions in the background of the charged magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Cher…
A non-trivial consequence of the super-correlator/super-amplitude duality is that the integrand of the four-point correlation function of stress-tensor multiplets in planar N=4 super Yang-Mills contains a certain combination of n-point amplitude integrands for any n. This combination is the sum of products of all helicity super-amplitudes with their corresponding helicity conjugates. The four-point correlator itself is described by a single scalar function whose loop level integrands possess a hidden permutation symmetry facilitating its computation up to ten loops. We discover that assuming Y…
