ANOMALOUS DIMENSIONS IN TURBULENCE

1991 ◽  
Vol 06 (11) ◽  
pp. 1023-1043 ◽  
Author(s):  
ALEXANDER A. MIGDAL
Keyword(s):  
Field Theory ◽  
Effective Action ◽  
Numerical Solutions ◽  
Gaussian Approximation ◽  
Planck Equation ◽  
Velocity Correlation ◽  
Scale Invariant ◽  
Numerical Work ◽  
Anomalous Dimensions ◽  
Independent Field

A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker—Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.

scholarly journals More on holographic correlators: twisted and dimensionally reduced structures

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Connor Behan ◽  
Pietro Ferrero ◽  
Xinan Zhou
Keyword(s):  
Field Theory ◽  
Theoretical Data ◽  
Infinite Family ◽  
Tree Level ◽  
Chiral Algebra ◽  
Perfect Agreement ◽  
Four Dimensions ◽  
Independent Field ◽  
Superconformal Theories ◽  
Emergent Structure

Abstract 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 formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals Conformal Symmetry in Field Theory and in Quantum Gravity

Universe ◽  
2018 ◽  
Vol 4 (11) ◽  
pp. 125 ◽  
Author(s):  
Lesław Rachwał
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Conformal Symmetry ◽  
Gravitational Theory ◽  
Fine Tuning ◽  
Conformal Anomaly ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Non Local

Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented.

scholarly journals Infinite dimensional Langevin equation and Fokker-Planck equation

1981 ◽  
Vol 81 ◽  
pp. 177-223 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Partial Differential Equations ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theory Theory ◽  
Quantum Field ◽  
Filtering Theory ◽  
Infinite Dimensional

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

scholarly journals GRAVITY DUAL FOR REGGEON FIELD THEORY AND NONLINEAR QUANTUM FINANCE

2009 ◽  
Vol 24 (32) ◽  
pp. 6197-6222 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Conformal Invariance ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Invariant ◽  
Galilean Invariance ◽  
Scale Invariant ◽  
Conformal Field ◽  
Nonlinear Quantum ◽  
Reggeon Field Theory

We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.

Numerical solutions for the spin-up of a stratified fluid

1982 ◽  
Vol 117 ◽  
pp. 71-90 ◽  
Author(s):  
Jae Min Hyun ◽  
William W. Fowlis ◽  
Alex Warn-Varnas
Keyword(s):  
Time Scale ◽  
Numerical Solutions ◽  
Side Wall ◽  
Stratified Fluid ◽  
Meridional Flow ◽  
Laser Doppler Velocimeter ◽  
Numerical Work ◽  
Diffusion Effects ◽  
Rate Of Decay ◽  
Flow Gradients

Numerical solutions for the impulsively started spin-up of a thermally stratified fluid in a cylinder with an insulating side wall are presented. Previous experimental and numerical work on stratified spin-up had not provided a comprehensive and accurate set of flow-field data. Further, comparisons of this work with theory showed, in general, a substantial discrepancy. The theory was scaled using the homogeneous meridional-flow spin-up time scale and thus viscous-diffusion effects were excluded from the interior. It was anticipated that these effects could only be significant on the larger viscous-diffusion time scale. However, the comparisons with theory showed a faster rate of decay for the measurements even over the shorter meridional-flow spin-up time scale. Previous workers had suggested a number of explanations but the cause of the discrepancy was still unresolved. To provide data to extend the previous work, a numerical model was used. The model was first checked against accurate experimental measurements of stratified spin-up made using a laser-Doppler velocimeter. New accurate results which cover ranges of Ekman number (5·92 × 10−4 ≤ E ≤ 7·24 × 10−4), Rossby number (0·019 ≤ ε ≤ 0·220), stratification parameter (0·0 ≤ Sa−1 ≤ 1·03), and Prandtl number (5·68 ≤ σ ≤ 7·10) are presented. These results show the radial and vertical structure of the decaying azimuthal and meridional flows. The inertial–internal gravity oscillations excited by the impulsive spin-up are clearly seen. By making use of conclusions from the previous work and the results presented in this paper, it is established that viscous diffusion in the interior is the cause of the discrepancy with theory. Stratification causes the meridional spin-up flow to be confined closer to the boundary disks. This results in non-uniform spin-up of the interior and hence flow gradients in the interior. These gradients introduce viscous diffusion into the interior sooner than anticipated by the theory. A previous suggestion that the faster decay rate is due to angular momentum being injected into the interior from an oscillation of the meridional corner-jet flow is shown to be untenable.

Sign in / Sign up

Export Citation Format

Share Document