Vortex strings and nonabelian sine-Gordon theories

We generalize the Lund-Regge model for vortex string dynamics in 4-dimensio nal Minkowski space to the arbitrary n-dimensional case. The n-dimensional vortex equation is identified with a nonabelian sine-Gordon equation and it s integrability is proven by finding the associated linear equations of the inverse scattering. An explicit expression of vortex coordinates in terms of the variables of the nonabelian sine-Gordon system is derived. In partic ular, we obtain the n-dimensional vortex soliton solution of the Hasimoto-t ype from the one soliton solution of the nonabelian sine-Gordon equation. ( C) 1999 Elsevier Science B.V. All rights reserved.