Coupled currents in cosmic strings

Abstract

We examine the structure of a cosmic string endowed with two Abelian neutral currents, associated with two global $U(1)$ symmetries. We first resolve the microstructure and show that it depends on two state parameters, namely, the squares of the phase gradients of the current carriers. We then provide a macroscopic description for such a string and show that it depends on an additional Lorentz-invariant state parameter that relates the two currents. We find that in most of the parameter space, the two-current string is essentially equivalent to the single-current-carrying string; i.e., only one field condenses onto the defect. In the regions where two currents are present, we find that as far as stability is concerned, one can approximate the dynamics with good accuracy using an analytic model based on either a logarithmic (on the electric side, i.e., for timelike currents) or a rational (on the magnetic side, i.e., for spacelike currents) world sheet Lagrangian. We end up by generalizing to the $N$ current case.