ar X iv : h ep - t h / 96 03 20 0 v 1 2 9 M ar 1 99 6 QMW - PH - 96 - 02 DUALITY INVARIANT MAGNETOHYDRODYNAMICS AND DYONS

The theory of magnetohydrodynamics is extended to the cases of a plasma of separate magnetic and electric charges, as well as to a plasma of dyons respectively. In both these cases the system possesses electric-magnetic duality symmetry. In the former case we find that because of the existence of two independent generalized Ohm’s law equations, the limit of infinite electric and magnetic conductivity results in the vanishing of both electric and magnetic fields, as well as the corresponding currents. In the dyonic case, we find that the resulting duality-invariant system of equations are equivalent to those of ordinary MHD, after suitable field redefinitions. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] Recently Polyakov [1] presented a new radical approach to the study of two dimensional (2d) turbulent fluids by proposing that certain conformal field theories (CFT) might offer a description of fully developed turbulence. Ferretti and Yang [2] applied these ideas to the effective field theory approximating 2d plasmasi.e., 2d magnetohydrodynamics (MHD). Recently we presented some new results [3] which extended the work of [2]. Strictly speaking, the theories studied in [2,3] were 3d MHD dimensionally reduced to 2d-i.e. all fields are taken to be independent of the third coordinate. In this way a generalized 2d MHD is obtained in which there are passive scalars as well as the usual velocity, electric and magnetic fields. Pure 2d MHD can be obtained by consistently setting to zero the passive scalars. In this letter, motivated by a desire to obtain even more generalized MHD equations in 2d, with a view to applying CFT techniques in looking for possible solutions in the turbulent regime [4], we shall construct the analogue of the MHD equations of plasmas that incorporate magnetic charges. Of course such theories like ordinary MHD, should find much broader physical applications. As we shall see there are at least three ways of accomplishing this. One could consider a purely magnetic plasma, consisting of oppositely charged magnetic monopoles. This is in fact the direct analogue of the usual plasma of electric charges (see e.g. [5]). Secondly we can consider a plasma where both types of charges are presenta kind of interacting pair of electric and magnetic plasmas. Finally, we may consider plasmas involving particles that carry both electric and magnetic chargesi.e. dyons. We shall see that all these possibilities can display MHD-like equations having different physical properties. Moreover all these possibilities are deeply connected with the idea of electric-magnetic duality. First we consider the situation where we have a plasma consisting of magnetic monopoles and their ionic counterparts “magneto-ions”. Following the well known methods (see for example [6]) that yield ordinary MHD in 3 dimensions, by deriving 1-fluid equations from the 2-fluid description, we shall obtain analogous “dual” MHD equations (referred to perhaps more appropriately as electrohydrodynamics in [5]). We begin with Maxwell’s equations including both electric and magnetic currents Je,Jm For example, there has been interesting recent work concerning the existence of electric string solutions in the MHD of magnetic monopole plasmas [5]