Turbulent Two Dimensional Magnetohydrodynamics and Conformal Field Theory.

TL;DR

This paper explores how non-unitary minimal models from conformal field theory can describe two-dimensional turbulent magnetohydrodynamics, revealing an infinite set of conserved quantities and deriving energy spectrum exponents.

Contribution

It introduces a novel application of non-unitary minimal models to 2D MHD turbulence, establishing a connection between conformal field theory and turbulent energy spectra.

Findings

Infinite conserved quantities in 2D-MHD turbulence.

Correlation functions derived using the M_{2,7} minimal model.

Energy spectrum exponents in the inertial range from 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.