Numerical study of the lowest-energy configurations for global string-antistring pairs.

We investigate the lowest energy configurations for string antistring pairs at fixed separations by numerically minimizing the energy. We show that for separations smaller than a critical value, a region of false vacuum develops in the middle due to large gradient energy density. Consequently, well defined string antistring pairs do not exist for such separations. We present an example of vortex antivortex production by vacuum bubbles where this effect seems to play a dynamical role in the annihilation of the pair. We also study the dependence of the energy of an string-antistring pair on their separation and find deviations from a simple logarithmic dependence for small separations. Present address: Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA