PERTURBING CONFORMAL TURBULENCE

We consider perturbations of the nonunitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of nonintegrable 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.