Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence

TL;DR

This paper develops a conformal field theory framework for steady state incompressible turbulence, linking anomalous scaling and intermittency to conformal anomalies and spontaneous symmetry breaking.

Contribution

It introduces a novel CFT-based model incorporating a dilaton to explain intermittency and anomalous scaling in turbulence across multiple dimensions.

Findings

Derives a KPZ-type equation for velocity structure functions.

Relates intermittency parameter to conformal anomaly coefficient.

Discusses entanglement entropy as a measure of intermittency.

Abstract

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent $z=\frac{2}{3}$. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.