Correlators Of Energy-momentum Tensor Research Articles

Cutoff AdS3 versus Toverline{T} CFT2 in the large central charge sector: correlators of energy-momentum tensor

In this article we probe the proposed holographic duality between Toverline{T} deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the Toverline{T} CFT in a Euclidean plane and 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 Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with Toverline{T} CFT parameters.

Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions.

A famous example of gauge-gravity duality is the result that the entropy density of the strongly coupled N=4 supersymmetric Yang-Mills theory in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at a finite-temperature T for all couplings λ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at λ=0 to exactly 4/5 of the Stefan-Boltzmann limit at λ=∞. Calculating the retarded energy-momentum tensor correlator in the scalar channel at λ=∞, I find that it has two logarithmic branch cuts originating at ω=±4Tln(1+sqrt[5]/2) but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic conformal field theories in 2+1 dimensions.

Type I Abelian Higgs strings: Evolution and cosmic microwave background constraints

We present results from the first simulations of networks of Type I Abelian Higgs cosmic strings to include both matter and radiation eras and Cosmic Microwave Background (CMB) constraints. In Type I strings, the string tension is a slowly decreasing function of the ratio of the scalar and gauge mass-squared, $\beta$. We find that the mean string separation shows no dependence on $\beta$, and that the energy-momentum tensor correlators decrease approximately in proportion to the square of the string tension, with additional O(1) correction factors which asymptote to constants below $\beta \lesssim 0.01$. Strings in models with low self-couplings can therefore satisfy current CMB bounds at higher symmetry-breaking scales. This is particularly relevant for models where the gauge symmetry is broken in a supersymmetric flat direction, for which the effective self-coupling can be extremely small. If our results can be extrapolated to $\beta \simeq 10^{-15}$, even strings formed at $10^{16}$ GeV (approximately the grand unification scale in supersymmetric extensions of the Standard Model) can be compatible with CMB constraints.

Large-scale messengers from massive higher spin fields

We show that nonperturbative production of massive higher spin fields from vacuum will accompany the generation of non-vanishing macroscopic energy-momentum tensor correlators. This argument is based on the general causal field formalism, which gives a manifestly covariant description of higher spin particles without any reference to gauge redundancy. Our findings are direct consequence of the Poincaré covariance and anlayticity of the Green’s functions and independent of any detailed particle physics model. Further, we discuss the idea that any mechanism causing imbalance between the on-shell production of left- and right-handed fields leads to a helical structure in the energy momentum correlators and violation of the macroscopic parity symmetry. We check our method for fields with spin frac{1}{2} and show that it correctly reproduces previous results. The formalism, however, suffers from pathologies related to non-localities that appear for massless particles with spin ≥ 1 in flat space. We discuss the origin of these pathologies and the relevance of our findings to cosmology.

Flow of the □R Weyl anomaly

An important aspect of Weyl anomalies is that they encode information on the irreversibility of the renormalisation group flow. We consider, $\Delta \bar b = \bar{b}^{\textrm{UV}} - \bar{b}^{\textrm{IR}}$, the difference of the ultraviolet and infrared value of the $\Box R$-term of the Weyl anomaly. The quantity is related to the fourth moment of the trace of the energy momentum tensor correlator for theories which are conformal at both ends. Subtleties arise for non-conformal fixed points as might be the case for infrared fixed points with broken chiral symmetry. Provided that the moment converges, $\Delta \bar{b}$ is then automatically positive by unitarity. Written as an integral over the renormalisation scale, flow-independence follows since its integrand is a total derivative. Furthermore, using a momentum subtraction scheme (MOM) the 4D Zamolodchikov- metric is shown to be strictly positive beyond perturbation theory and equivalent to the metric of a conformal manifold at both ends of the flow. In this scheme $\bar{b}(\mu)$ can be extended outside the fixed point to a monotonically decreasing function. The ultraviolet finiteness of the fourth moment enables us to define a scheme for the $\delta {\cal L} \sim b_0 R^2$-term, for which the $R^2$-anomaly vanishes along the flow. In the MOM- and the $R^2$-scheme, $\bar{b}(\mu)$ is shown to satisfy a gradient flow type equation. We verify our findings in free field theories, higher derivative theories and extend $\Delta \bar{b}$ and the Euler flow $\Delta \beta_a$ for a Caswell-Banks-Zaks fixed point for QCD-like theories to next-to-next-to leading order using a recent $\langle G^2G^2 \rangle$-correlator computation.

Kubo formulas for the shear and bulk viscosity relaxation times and the scalar field theory shear τπ calculation

In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times, respectively. They are found by examining response functions of the stress-energy tensor. We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode. We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of computing both the shear and bulk viscosity relaxation times. Next, we calculate the shear viscosity relaxation time using the diagrammatic approach in the Keldysh basis for the massless $\lambda\phi^4$ theory. We derive a respective integral equation which enables us to compute $\eta\tau_\pi$ and then we extract the shear relaxation time. The relaxation time is shown to be inversely related to the thermal width as it should be.

From strong to weak coupling in holographic models of thermalization

We investigate the analytic structure of thermal energy-momentum tensor correlators at large but finite coupling in quantum field theories with gravity duals. We compute corrections to the quasinormal spectra of black branes due to the presence of higher derivative $R^2$ and $R^4$ terms in the action, focusing on the dual to $\mathcal{N}=4$ SYM theory and Gauss-Bonnet gravity. We observe the appearance of new poles in the complex frequency plane at finite coupling. The new poles interfere with hydrodynamic poles of the correlators leading to the breakdown of hydrodynamic description at a coupling-dependent critical value of the wave-vector. The dependence of the critical wave vector on the coupling implies that the range of validity of the hydrodynamic description increases monotonically with the coupling. The behavior of the quasinormal spectrum at large but finite coupling may be contrasted with the known properties of the hierarchy of relaxation times determined by the spectrum of a linearized kinetic operator at weak coupling. We find that the ratio of a transport coefficient such as viscosity to the relaxation time determined by the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the vicinity of infinite coupling but flattens out for weaker coupling, suggesting an extrapolation from strong coupling to the kinetic theory result. We note that the behavior of the quasinormal spectrum is qualitatively different depending on whether the ratio of shear viscosity to entropy density is greater or less than the universal, infinite coupling value of $\hbar/4\pi k_B$. In the former case, the density of poles increases, indicating a formation of branch cuts in the weak coupling limit, and the spectral function shows the appearance of narrow peaks. We also discuss the relation of the viscosity-entropy ratio to conjectured bounds on relaxation time in quantum systems.

Shear viscosity of theΦ4theory from classical simulation

Shear viscosity of the classical $\Phi^4$ theory is measured using classical microcanonical simulation. To calculate the Kubo formula, we measure the energy-momentum tensor correlation function, and apply the Green-Kubo relation. Being a classical theory, the results depend on the cutoff which should be chosen in the range of the temperature. Comparison with experimentally accessible systems is also performed.

Regularization of energy-momentum tensor correlators and parity-odd terms

We discuss the problem of regularizing correlators in conformal field theories. The only way to do it in coordinate space is to interpret them as distributions. Unfortunately except for the simplest cases we do not have tabulated mathematical results. The way out we pursue here is to go to momentum space and use Feynman diagram techniques and their regularization methods. We focus on the energy-momentum tensor correlators and, to gain insight, we compute and regularize 2-point functions in 2d with various techniques both in coordinate space and in momentum space, obtaining the same results. Then we do the same for 2-point functions in 4d. Finally we turn to 3-point function in 4d, and concentrate on the parity-odd part. We derive in particular the regularized trace and divergence of the energy-momentum tensor in a chiral fermion model. We discuss the problems related to the parity-odd trace anomaly.

Bulk and shear viscosities of hot and dense hadron gas

We estimate bulk and shear viscosity at finite temperature and baryon densities of hadronic matter within hadron resonance gas model. For bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For shear viscosity coefficient, we estimate the same using molecular kinetic theory to relate the shear viscosity coefficient to average momentum of the hadrons in the hot and dense hadron gas. The bulk viscosity to entropy ratio increases with chemical potential and is related to the reduction of velocity of sound at nonzero chemical potential. The shear viscosity to entropy ratio on the other hand, shows a nontrivial behavior with the ratio decreasing with chemical potential for small temperatures but increasing with chemical potential at high temperatures and is related to decrease of entropy density with chemical potential at high temperature due to finite volume of the hadrons.

OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order

The correlator of two gluonic operators plays an important role for example in transport properties of a Quark Gluon Plasma (QGP) or in sum rules for glueballs. In [1] an operator product expansion (OPE) at zero temperature was performed for the correlators of two scalar operators $O_1=-\frac{1}{4} G^{\mu \nu}G_{\mu \nu}$ and two QCD energy-momentum tensors $T^{\mu\nu}$. There we presented analytical two-loop results for the Wilson coefficient $C_1$ in front of the gluon condensate operator $O_1$. In this paper these results are extended to three-loop order. The three-loop Wilson coefficient $C_0$ in front of the unity operator $O_0=1$ was already presented in [1] for the $T^{\mu\nu}$-correlator. For the $O_1$-correlator the coefficient $C_0$ is known to four loop order from [2]. For the correlator of two pseudoscalar operators $\tilde{O}_1=\varepsilon_{\mu\nu\rho\sigma} G^{\mu \nu} G^{\rho \sigma}$ both coefficients $C_0$ and $C_1$ were computed in [3] to three-loop order. At zero temperature $C_0$ and $C_1$ are the leading Wilson coefficients in massless QCD.

Holographic thermalization in [Formula: see text] super Yang-Mills theory at finite coupling.

We investigate the behavior of energy-momentum tensor correlators in holographic {mathcal N}=4 super Yang–Mills plasma, taking finite coupling corrections into account. In the thermal limit we determine the flow of quasinormal modes as a function of the ’t Hooft coupling. Then we use a specific model of holographic thermalization to study the deviation of the spectral densities from their thermal limit in an out-of-equilibrium situation. The main focus lies on the thermalization pattern with which the plasma constituents approach their thermal distribution as the coupling constant decreases from the infinite coupling limit. All obtained results point towards the weakening of the usual top-down thermalization pattern.

OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order

In this paper analytical results are presented for higher order corrections to coefficient functions of the operator product expansion (OPE) for the correlator of two pseudoscalar gluonium operators $ {{\mathop{O}\limits^{\sim}}_1}={G^{{\mu v}}}\;{{\mathop{G}\limits^{\sim}}_{{\mu v}}} $ . The Wilson coefficient in front of the scalar gluon condensate operator $ {O_1}=-\frac{1}{4}{G^{{\mu v}}}{G_{{^{{\mu v}}}}} $ is given at three-loop accuracy. The leading coefficient C 0 in front of the unity operator O 0 = 1 has been calculated up to three-loop order some time ago [1] but has been checked independently in this work. It is interesting to see that the coefficient C 1 in the pseudoscalar case is finite, whereas contact terms appear in C 0 in this case and in both coefficients C 0 and C 1 in the cases of the scalar gluonium correlator and the energy momentum tensor correlator [2]. For the corresponding Renormalization Group invariant Wilson coefficients which are also constructed the results are partially extended to four-loop accuracy. All results are given in the $ \overline{\mathrm{MS}}-\mathrm{scheme} $ at zero temperature.

Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory

We investigate the behavior of energy momentum tensor correlators in strongly coupled large-N_c Yang-Mills theory at nonzero temperature, working within the Improved Holographic QCD model. In particular, we determine the spectral functions and corresponding imaginary time correlators in the bulk and shear channels, and compare the results to recent perturbative and lattice calculations where available. For the bulk channel imaginary time correlator, for which all three results exist, lattice data is seen to favor the holographic prediction over the perturbative one over a wide range of temperatures.

OPE of the energy-momentum tensor correlator in massless QCD

We analytically calculate higher order corrections to coefficient functions of the operator product expansion (OPE) for the Euclidean correlator of two energy-momentum tensors in massless QCD. These are the three-loop contribution to the coefficient C_0 in front of the unity operator O_0=1 and the one and two-loop contributions to the coefficient C_1 in front of the gluon "condensate" operator O_1=-1/4 G^{\mu \nu} G_{\mu \nu}. For the correlator of two operators O_1 we present the coefficient C_1 at two-loop level.

Shear modes, criticality and extremal black holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.

Transport coefficients at zero temperature from extremal black holes

Using the AdS/CFT correspondence we study transport coefficients of a strongly-coupled (2 +1)-dimensional field theory at {\it zero} temperature and finite charge density. The field theory under consideration is dual to the extremal Reissner-Nordstrom AdS_4 black hole in the bulk. We show that, like the cases of scalar and spinor operators studied in \cite{Faulkner:2009wj}, the correlators of charge (vector) current and energy-momentum (tensor) operators exhibit scaling behavior at low frequency. The existence of such low frequency behavior is related to the fact that the near-horizon geometry of the extremal black hole background has an AdS_2 factor. We carefully calculate the shear viscosity (at zero temperature) and show that the ratio of the shear viscosity to the entropy density takes the value of 1/4\pi. Because of the AdS_2 factor, we argue that this result stays the same for all d-dimensional boundary field theories dual to the extremal Reissner-Nordstrom AdS_{d+1} black holes. Also, we compute the charge conductivity at zero temperature. The limiting behavior of the conductivity for small frequencies is also attributed to the near horizon AdS_2 factor and is argued to hold regardless of the dimension of the zero-temperature boundary field theory. Finally, using the extremal dyonic AdS_4 black hole as the background, we extract the conductivity in the presence of a constant magnetic field.

Cutoff effects on energy-momentum tensor correlators in lattice gauge theory

We investigate the discretization errors affecting correlators of the energy-momentum tensor Tμν at finite temperature in SU(Nc) gauge theory with the Wilson action and two different discretizations of Tμν. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time x0 and spatial momentum p, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy ∫d3x T00 has much larger discretization errors than the correlator of momentum ∫d3x T0k. Secondly, the shear and diagonal stress correlators (T12 and Tkk) require Nτ ⩾ 8 for the Tx0 = ½ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with aσ/aτ = 2 are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite p correlators.

Energy-momentum tensor correlators and spectral functions

We calculate the thermal Euclidean correlators and the spectral functions of the energy-momentum tensor for pure gauge theories, including at non-zero spatial momentum, at leading order in perturbation theory. Our goal is to improve the extraction of transport properties from Euclidean correlators that are computable in lattice QCD. Based on our results and the predictions of hydrodynamics for the structure of the spectral functions at low frequencies, we show that the shear and bulk viscosities can advantageously be extracted from the Euclidean correlators of the conserved charges, energy and momentum, at small but non-vanishing spatial momentum. The spectral functions in these channels are free of the ultraviolet $\omega^4$ term which represents a large background to the thermal physics encoded in the correlators of the fluxes.

Calculating the infrared central charges for perturbed minimal models: improving the RG perturbation

We illustrate a method for improving Renormalisation Group improved perturbation theory by calculating the infrared central charge of a perturbed conformal field theory. The additional input is a dispersion relation that exploits analyticity of the energy-momentum tensor correlator.