Hyperlogarithms in the theory of turbulence of infinite dimension

Abstract

Parametric integration with hyperlogarithms so far has been successfully used in problems of high energy physics (HEP) and critical statics. In this work, for the first time, it is applied to a problem of critical dynamics, namely, a stochastic model of developed turbulence in high-dimensional spaces, which has a propagator that is non-standard with respect to the HEP: $(-i\omega +\nu k^2{)}^{-1}$. Adaptation of the hyperlogarithm method is carried out by choosing a proper renormalization scheme and considering an effective dimension of the space. Analytical calculation of the renormalization group functions is performed up to the fourth order of the perturbation theory, $\epsilon$-expansion of the critical exponent $\omega$ responsible for the infrared stability of the fixed point is obtained.

arXiv comment16 pages

References in corpus (21)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• High-precision calculation of the 4-loop contribution to the electron g-2 in QED
• The massless higher-loop two-point function
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar
• Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
• Feynman integrals and hyperlogarithms
• On hyperlogarithms and Feynman integrals with divergences and many scales
• Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation
• Four-loop quark form factor with quartic fundamental colour factor
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
• Two-loop calculation of the turbulent Prandtl number
• The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion
• Diagram Reduction in Problem of Critical Dynamics of Ferromagnets: 4-Loop Approximation
• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
• Renormalization group in the infinite-dimensional turbulence: third-order results
• Field-theoretic analysis of directed percolation: Three-loop approximation
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model

Cited by in corpus (1)

• Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum