A Logarithmic Conformal Field Theory Solution For Two Dimensional Magnetohydrodynamics In Presence of The Alf'ven Effect

TL;DR

This paper develops a logarithmic conformal field theory model to describe two-dimensional magnetohydrodynamics with the Alfvén effect, revealing unique theoretical insights into the energy spectrum and correlation functions.

Contribution

It introduces a specific logarithmic conformal field theory solution with a calculated central charge and energy spectrum for magnetohydrodynamics with the Alfvén effect, expanding theoretical understanding.

Findings

Identifies a unique conformal field theory with central charge c=-209/7.

Derives the energy spectrum as E(k) ~ k^(-13/7) log(k).

Highlights the role of logarithmic terms in correlation functions.

Abstract

When Alf`ven effect is peresent in magnetohydrodynamics one is naturally lead to consider conformal field theories, which have logarithmic terms in their correlation functions. We discuss the implications of such logarithmic terms and find a unique conformal field theory with centeral charge $c=-\frac{209}{7}$, within the border of the minimal series, which satisfies all the constraints. The energy espectrum is found to be \newline $E(k)\sim k^{-\frac{13}{7}} \log{k}$.