Turbulent Two Dimensional Magnetohydrodynamics and Conformal Field Theory.

Abstract

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 Alf'ven effect or equivelently 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.

21 pages, Latex , no Figures, 2 Tables.

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