Scale Dependent Intermittency and Conformal Invariance in Turbulence

We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of scales. In the simplest case, the theory leads to the log-normal model. Parameters of the model are expressed via integrals of the conformal correlation functions. Non-Gaussian conformal correlation functions of high order are studied.