5 v 1 2 9 N ov 1 99 6 An exact solution of the loop equation in strong turbulence

The Hamilton-Jacobi equation for the loop effective action in strong turbulence with Gaussian random forces [1,2] is solved by making use of the smearing procedure for the loop space functional Laplacian, proposed in [3]. The solution obtained satisfies tensor-or scalar area law ansatz and depends on the initial data and the potential term in the loop Hamiltonian, averaged over loops. In the lowest order in the viscosity this average may be eliminated, and the solution is given by a certain linear combination of the initial data and the potential term and their functional derivatives.