Logarithmic Conformal Field Theory Solutions of Two Dimensional Magnetohydrodynamics

TL;DR

This paper applies logarithmic conformal field theory to find solutions for turbulent phases in 2D magnetohydrodynamics, revealing new symmetries and solutions derived from minimal models.

Contribution

It introduces a novel approach using logarithmic conformal field theory to solve turbulence equations in 2D magnetohydrodynamics, highlighting hidden symmetries and primary fields.

Findings

Solutions to Hopf equations are obtained within the logarithmic CFT framework.

The approach uncovers continuous hidden symmetries in the models.

Distinct primary fields of specific dimensions are identified.

Abstract

We consider the application of logarithmic conformal field theory in finding solutions to the turbulent phases of 2-dimensional models of magnetohydrodynamics. These arise upon dimensional reduction of standard (infinite conductivity) 3-dimensional magnetohydrodynamics, after taking various simplifying limits. We show that solutions of the corresponding Hopf equations and higher order integrals of motion can be found within the solutions of ordinary turbulence proposed by Flohr, based on the tensor product of the logarithmic extension ${\tilde c}_{6,1} $ of the non-unitary minimal model $c_{6,1} $. This possibility arises because of the existence of a continuous hidden symmetry present in the latter models, and the fact that there appear several distinct dimension -1 and -2 primary fields.