  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.
