Cosmic-string loops are straight

It is shown that a loop of idealized cosmic string deforms the background geometry in its vicinity so that its path and shape become geodesics of this background. For angular deficits smaller than π, this deformation causes the background curvature to grow without bound near an infinitely thin string. However, the rate of growth is so weak that the tidal forces are not yet appreciable at the surface of a grand-unification string. Although equations of motion for the string in a ‘‘background’’ geometry cannot be defined in a clear-cut fashion, they are not inconsistent with the conventional dynamics derived from the Nambu action.