Dual strings and magnetohydrodynamics

We investigate whether dual strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the dual string equations (with a non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields. It is shown that the energy-momentum tensor for the dual string can be reinterpreted as an energy-momentum tensor for magnetohydrodynamics, provided certain conditions are satisfied. We also give a brief discussion of the case when magnetic monopoles are included, and indicate how this can lead to a non-relativistic ”electrohydrodynamics” picture of confinement. NBI-HET-9536 hep-th/9509023 E-mail: [email protected] A conducting gas/fluid interacting with a magnetic field is described by magnetohydrodynamics (see ref. [1] for a review of this subject). A turbulent plasma has a strong tendency to become extremely intermittent, because the vorticity concentrates in thin vortex tubes, and the magnetic field concentrates in thin flux tubes. When one looks at computer simulations [2] of such a plasma, the situation looks very ”stringy”, in the sense of an intermittent network of ”string”-like objects. This suggested to the author that it would be an interesting question to ask if dual strings (see e.g. the reviews mentioned in ref. [3]) could be solutions to the magnetohydrodynamics equations. In the following we shall assume that the conductivity is infinite, and the viscosity vanishes. In computer simulations one sees [2] that the flux tubes are formed as parallel magnetic field lines over a long scale, but then the field lines spread out and the magnetic field becomes diffuse and weak. After some distance the field lines may again join in a flux tube. The diffuse behavior is not ”string”-like, and is therefore from the very beginning not covered by our considerations. We do therefore not claim that all features considered in the following are realistic, but we hope that some of our results are of interest. In order to have a ”stringy” situation, we consider flux tubes which are closed (or have an infinite length). We also assume that they move with the velocity of the fluid at any point. This puts severe restrictions on the dynamics to which our picture applies. In particular, we expect that the magnetic energy is roughly of the same order as the kinetic energy of the gas/fluid. One case where our considerations may be of direct use, is the case where somehow closed magnetic flux tubes are generated in the early universe, e.g. as defects in some phase transition. Then these flux tubes are expected to follow the Nambu-Goto string equations [3]-[4], at least to the first approximation. On the other hand, these tubes should also follow the magnetohydrodynamics equations, since such flux tubes interact with the charged particles. Thus, if these closed flux tubes are to keep their identity for some time (ultimately they are expected to decay), the Nambu-Goto string equations and the magnetohydrodynamics equations should be satisfied. Now the results in the following indicate that it is indeed possible to satisfy both set of equations at the same time. We start by considering a magnetic field in the form of an infinitely narrow flux tube