Logarithmic conformal field theory solutions of two dimensional magnetohydrodynamics

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 extensionc 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. 1

Holographic applications of logarithmic conformal field theories

“…Log CFTs have appeared in a number of different contexts in condensed matter physics and related subjects, like two-dimensional turbulence [189][190][191] (see also [192][193][194]), Abelian sandpile models [195][196][197][198][199][200][201][202][203][204][205], critical polymers [17,18,24,[206][207][208][209][210], D-brane recoil [211][212][213][214][215][216] or decay [217], fractional quantum-Hall effect [218][219][220][221], gravitational dressing [222], percolation [35,[223][224][225][226][227], symplectic fermions [228], and systems with disorder [229][230][231]…”

Operator product expansion in logarithmic conformal field theory

“…Sometimes, longstanding puzzles in the description of certain theoretical models could be resolved, e.g. the Haldane-Rezayi state in the fractional quantum Hall effect [28,7,70], multi-fractality [12], or two-dimensional conformal turbulence [18,66,76]. Other applications worth mentioning are gravitational dressing [5], polymers and abelian sandpiles [74,33,8,57], the (fractional) quantum Hall effect [17,31,49], and -perhaps most importantly -disorder [9,43,56,29,10,69,30,3,4].…”

Bits and Pieces in Logarithmic Conformal Field Theory

“…Sometimes, longstanding puzzles in the description of certain theoretical models could be resolved, e.g. the enigmatic degeneracy of the ground state in the Haldane-Rezayi fractional quantum Hall effect with filling factor ν = 5/2, where conformal field theory descriptions of the bulk theory proved difficult [11,49,102], multi-fractality in disordered Dirac fermions, where the spectra did not add up correctly as long as logarithmic fields in internal channels were neglected [17], or two-dimensional conformal turbulence, where Polyakov's proposal of a conformal field theory solution did contradict phenomenological expectations on the energy spectrum [35,98,109]. Other applications worth mentioning are gravitational dressing [8], polymers and Abelian sandpiles [13,56,84,106], the (fractional) quantum Hall effect [34,53,74], and -perhaps most importantly -disorder [5,6,14,15,50,51,68,83,101].…”