Mirror symmetry breaking in toy models of developed turbulence

Abstract

Importance of symmetry considerations in high energy physics and statistical systems in critical region is discussed. As a concrete example, the field theoretic renormalization group technique is applied to a general A model of active vector admixture b. Parameter A represents a continuous real parameter that governs the interaction structure of the system. The model encompasses the physically most relevant magnetohydrodynamic scenario (A = 1), and the model of linearized Navier-Stokes equations (A = -1). The environment is assumed to be in a state of fully developed turbulence, i.e. Reynolds number takes an infinite value. Additionally, spatial parity breaking is incorporated via the continuous parameter ρ. Studied system exhibits instability with respect to it, and large-scale generation of non-zero mean value b is observed. This is then explained in terms of spontaneous symmetry breaking mechanism.