Strings of opposite magnetic charges in a gauge field theory

We show that there are soliton-like solutions representing arbitrarily located M vortices and N antivortices with opposite magnetic charges in an Abelian gauge field theory. We establish an existence and uniqueness theorem and prove that the total magnetic flux is proportional to M -N but the total energy is proportional to M + N. In the presence of Einstein's gravity, we establish an existence theorem under a necessary and sufficient condition that ensures the geodesic completeness of the corresponding gravitational metric. The coexisting vortices and antivortices are now cosmic strings and antistrings and the total magnetic flux and matter-gauge energy are given by similar expressions as those for vortices. Besides the energy, the total curvature also provides an exact, quantized measurement of the number of the strings of the two types.