Turbulent two-dimensional magnetohydrodynamics and conformal field theory

We show that an infinite number of non-unitary minimal models may describe two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and absence of the Alf'ven effect. We argue that the existence of a critical dynamical index results in the Alfven effect or equivalently the equipartition of energy. We show that there are an infinite number of conserved quantities in 2D - MHD turbulent systems both in the limit of vanishing the viscocities and in force free case. In the force free case, using the non-unitary minimal model M(2,7) we derive the correlation functions for the velocity stream Function and magnetic flux function. Generalising this simple model we find the exponents of the energy spectrum in the inertial range for a class of conformal field theories. (C) 1996 Academic Press, Inc.