Stress Tensor Correlation Functions Research Articles

Renormalization group flows in AdS and the bootstrap program

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.

Field Theory of Interacting Boundary Gravitons

Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by GG and \LambdaΛ. As a consequence, correlation functions of the boundary stress tensor in AdS_33 are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS_33 gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a T\overline{T}TT¯-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order (GG being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

Holographic boundary actions in AdS3/CFT2 revisited

The generating functional of stress tensor correlation functions in two-dimensional conformal field theory is the nonlocal Polyakov action, or equivalently, the Liouville or Alekseev-Shatashvili action. I review its holographic derivation within the AdS3/CFT2 correspondence, both in metric and Chern-Simons formulations. I also provide a detailed comparison with the well-known Hamiltonian reduction of three-dimensional gravity to a flat Liouville theory, and conclude that the two results are unrelated. In particular, the flat Liouville action is still off-shell with respect to bulk equations of motion, and simply vanishes in case the latter are imposed. The present study also suggests an interesting re-interpretation of the computation of black hole spectral statistics recently performed by Cotler and Jensen as that of an explicit averaging of the partition function over the boundary source geometry, thereby providing potential justification for its agreement with the predictions of a random matrix ensemble.

Relationship between the Relaxation of Ionic Liquid Structural Motifs and That of the Shear Viscosity.

In a set of recent articles, we have highlighted that friction is highly inhomogeneous in a typical ionic liquid (IL) with charge networks that are stiff and charge-depleted regions that are soft. This has consequences not only for the dynamics of ILs but also for the transport properties of solutes dissolved in them. In this article, we explore whether the family of alkylimidazolium ILs coupled with bis(trifluoromethylsulfonyl)imide (with similar Coulombic interactions but different alkyl tails), when dynamically “equalized” by having a similar shear viscosity, display q-dependent structural relaxation time scales that are the same across the family. Our results show that this is not the case, and in fact, the relaxation of in-network charge alternation appears to be significantly affected by the presence of separate polar and apolar domains. However, we also find that if one was to assign weight factors to the relaxation of the structural motifs, charge alternation always contributes about the same amount (between 62.1 and 66.3%) across systems to the running integral of the stress tensor correlation function from which the shear viscosity is derived. Adjacency correlations between positive and negative moieties also contribute an identical amount if a prepeak is not present (about 38%) and a slightly smaller amount (about 28%) when intermediate range order exists. The prepeak only contributes about 6% to viscoelastic relaxation, highlighting that the dynamics of the smaller scale motifs is the most important.

Multiplicative noise and the diffusion of conserved densities

Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.

Scattering mechanisms, relaxation times, and shear viscosity in universal anomalous transport of unitary Fermi gases

In this paper we investigate the scattering mechanisms of viscous momentum transport in unitary Fermi gases below the pseudogap temperature T* by opening almost all the elastic and inelastic scattering channels. For a given system Hamiltonian, we adopt a microscopic t-matrix approximation to determine the thermodynamical quantities, and we approach an equivalent three-fluid dynamics to calculate the viscous relaxation time τ by two kinds of elementary excitations. The exotic scattering processes raised by uncondensed Fermi pairs greatly decay τ and lead to a universal behavior of τ with temperature, which is closely related to the anomalous transport in a wide range of strongly correlated systems. For linking our findings of τ to the shear viscosity η, we present a Kubo-based expression of η by the stress-tensor correlation function with conserved vertex corrections, and we give an approximate relation for a possible experimental determination of τ. Our results fit well with measurements and are comparable with other theories. Moreover, we verify the newly proposed universal upper bound of the ratio of η and entropy density s in unitary Fermi gases.

Universality of Squashed-Sphere Partition Functions

We present several results concerning the free energy of odd-dimensional conformal field theories (CFTs) on squashed spheres. First, we propose a formula which computes this quantity for holographic CFTs dual to higher-curvature gravities with second-order linearized equations of motion. As opposed to standard on-shell action methods for Taub geometries, our formula only involves a simple evaluation of the corresponding bulk Lagrangian on an auxiliary pure anti-de Sitter (AdS) space. The expression is closely related to the function determining the possible AdS vacua of the bulk theory in question, which we argue to act as a generating functional from which correlation functions of the boundary stress tensor can be easily characterized. Finally, based on holographic results and free-field numerical calculations, we conjecture that the subleading term in the squashing-parameter free-energy expansion is universally controlled by the stress-tensor three-point function charge t_{4} for general (2+1)-dimensional CFTs.

N -point functions of strongly coupled fluids dual to generalized higher-derivative theories of gravity

We calculate the connected stress-tensor correlation functions that are dual to a certain class of graviton scattering amplitudes in an asymptotically anti-de Sitter, black brane spacetime. This is a continuation of a previous study in which one-particle-irreducible amplitudes were calculated for arbitrarily higher-derivative gravity in a particular kinetic regime of high energies and large scattering angles. The utility of this regime is twofold: It is particularly well suited for translating scattering amplitudes into the language of the gauge theory and it emphasizes the contributions from higher-derivative corrections (which would otherwise be perturbatively suppressed). Using the new results, we show how it could be possible to identify, experimentally, the gravitational dual to a strongly coupled fluid such as the quark-gluon plasma.

Holographic calculation of two-point correlation functions of CFT stress tensor in the BMS gauge and flat-space holography

In this paper, we use the holographic renormalization method to calculate the two-point correlation functions of the CFT stress tensor. In the gravity side, we write the asymptotically AdS spacetimes in the BMS gauge and apply the standard holographic renormalization method for these space-times. The significance of using multi-point functions in this gauge is that its flat-space limit is well-defined. We discuss this point in the last section of the paper.

Einstein gravity 3-point functions from conformal field theory

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

ABJ quadrality

We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d mathcal{N}=6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS4 × ℂℙ3 and mathcal{N}=6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS4. After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N1) × USp(2N2) while the background of the string theory is replaced by AdS4 × ℂℙ3/Z2, and the supersymmetries in the both theories reduce to mathcal{N}=5 . We propose that adding the orientifolds to the mathcal{N}=6 Vasiliev theory leads to mathcal{N}=5 SUSY Vasiliev theory. It turns out that the mathcal{N}=5 case is more involved because there are two formulations of the mathcal{N}=5 Vasiliev theory with either O or USp internal symmetry. We show that the two mathcal{N}=5 Vasiliev theories can be understood as certain projections of the mathcal{N}=6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N1) × USp(2N2) ABJ theory has the two vector model like limits: N2 ≫ N1 and N1 ≫ N2 which correspond to the semi-classical mathcal{N}=5 Vasiliev theories with O(N1) and USp(2N2) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the mathcal{N}=5 ABJ theory, string/M-theory and two mathcal{N}=5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the mathcal{N}=5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the mathcal{N}=6 Vasiliev theory and the parameters in the mathcal{N}=6 ABJ theory, which was conjectured in [1].

Transport coefficients of normal liquid helium-4 calculated by path integral centroid molecular dynamics simulation

Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7–4.0K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.

Boundary anomalies and correlation functions

It was shown recently that boundary terms of conformal anomalies recover the universal contribution to the entanglement entropy and also play an important role in the boundary monotonicity theorem of odd-dimensional quantum field theories. Motivated by these results, we investigate relationships between boundary anomalies and the stress tensor correlation functions in conformal field theories. In particular, we focus on how the conformal Ward identity and the renormalization group equation are modified by boundary central charges. Renormalized stress tensors induced by boundary Weyl invariants are also discussed, with examples in spherical and cylindrical geometries.

Holographic renormalization of 3D minimal massive gravity

We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.

Universal stress-tensor correlation functions of strongly coupled conformal fluids

We have shown in two accompanying papers that, for Einstein gravity, the graviton multi-point functions are universal in a particular kinematic region and depend only on the (generalized) Mandelstam variable s. The effects of the leading corrections to Einstein gravity were shown to be similarly universal, inducing a specific difference in the angular dependence. Here we show, relying on the gauge–gravity duality, that the stress-tensor correlation functions of conformal fluids whose gravitational dual is either Einstein gravity or its leading correction are also universal. We discuss the possible significance of these results to multi-particle correlations in heavy-ion collisions. We show that, to test our ideas, the stress-energy correlation functions have to measured rather than the standard multiplicity correlation functions. We then discuss schematically how stress-energy correlations in heavy-ion collisions can be used to test our findings. We argue that, if these correlations can be measured precisely enough, they will provide a unique way to probe the existence of a gravitational dual to the quark–gluon plasma and to determine its universality class.

Green–Kubo relations for dynamic interfacial excess properties

In this paper we analyze the fluctuations of the in-plane interfacial excess fluxes in multiphase systems, in the context of the extended irreversible thermodynamics formalism. We derive expressions for the time correlation functions of the surface extra stress tensor, the surface mass flux vector, and the surface energy flux vector, and use these expressions to derive Green–Kubo relations for the surface shear viscosity, the surface dilatational viscosity, the surface diffusion coefficient, and the surface thermal conductivity. These Green-Kubo relations can be used to compute these excess transport coefficients using for example molecular dynamics simulations.

Holographic predictions for cosmological 3-point functions

AbstractWe present the holographic predictions for cosmological 3-point correlators, involving both scalar and tensor modes, for a universe which started in a non-geometric holographic phase. Holographic formulae relate the cosmological 3-point functions to stress tensor correlation functions of a holographically dual three-dimensional non-gravitational QFT. We compute these correlators at 1-loop order for a theory containing massless scalars, fermions and gauge fields, and present an extensive analysis of the constraints due to Ward identities showing that they uniquely determine the correlators up to a few constants. We define shapes for all cosmological bispectra and compare the holographic shapes to the slow-roll ones, finding that some are distinguishable while others, perhaps surprisingly, are not. In particular, for three gravitons, we are able to recover the slow-roll shapes exactly.

On graviton non-gaussianities during inflation

We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum [1106.3228, 1108.0175], even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization. These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.

Minkowski vacuum stress tensor fluctuations

We study the fluctuations of the stress tensor for a massless scalar field in two- and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of derivatives of a scalar function. These expressions allow one to express spacetime averages of the correlation function as finite integrals. We also study the correlation between measurements of the energy density along a world line. We find that these measurements may be either positively correlated or anticorrelated. The anticorrelated measurements can be interpreted as telling us that, if one measurement yields one sign for the averaged energy density, a successive measurement with a suitable time delay is likely to yield a result with the opposite sign.

Energy flux correlations and moving mirrors

We study the quantum stress tensor correlation function for a massless scalar field in a flat two-dimensional spacetime containing a moving mirror. We construct the correlation functions for right-moving and left-moving fluxes for an arbitrary trajectory, and then specialize them to the case of a mirror trajectory for which the expectation value of the stress tensor describes a pair of delta-function pulses, one of negative energy and one of positive energy. The flux correlation function describes the fluctuations around this mean stress tensor, and reveals subtle changes in the correlations between regions where the mean flux vanishes.