TURBULENT TWO DIMENSIONAL MANGETOHYDRODYNAMICS AND CONFORMAL FIELD THEORY
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Abstract:
We generalise Polyakov's method of describing two dimensional turbulence using conformal field theory to the case of two dimensional magnetohydrodynamics. We show that an infinite number of non-unitary minimal models may describe the two dimensional magnetohydrodynamics, both when the Alf'ven effect is present and in its absence. We argue that the existence of a critical dynamical index results in the Alf'ven effect or the equipartition of energy. We show that there are an infinite number of conserved quantities in 2D \Gamma MHD turbulent system. 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 the simple model we find the exponents of the energy spectrum in the inertial range, for a class of conformal field theories. There has been some recent activity towards the application of Conformal Field Theory (CFT) to the theory of turbulence in two dimensions [1-7]. The main point is that the
Citations
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