Perturbing Conformal Turbulence

TL;DR

This paper investigates how perturbations affect two-dimensional conformal turbulence models, deriving constraints on perturbing operators and showing invariance of the Hopf equation under certain perturbations.

Contribution

It provides new constraints on perturbations in conformal turbulence and demonstrates the invariance of the Hopf equation under specific first-order perturbations.

Findings

Constraints on perturbing operator dimensions derived

Hopf equation shown to be invariant under certain perturbations

Examples illustrating the theoretical results provided

Abstract

We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the dimension of the perturbing operator. We give some general solutions of these constraints, illustrating with examples of specific models. We also examine the effect of such perturbations on the Hopf equation and derive the interesting result that the latter is invariant under a certain class of perturbations, to first order in perturbation theory, examples of which are given in specific cases.