SEMILOCAL STRING FORMATION IN 2 DIMENSIONS

We present a toy model for the investigation of the formation of semil ocal strings, where a planar symmetry is employed to reduce the system to two dimensions. We approximate the symmetry breaking using an exte nsion of the Vachaspati-Vilenkin algorithm, where we throw down random phases for the scalar fields and then find the gauge field configurat ion which minimizes gradient energy in this fixed scalar background, W e show this procedure reproduces the standard estimate for the formati on rate of cosmic strings. For semilocal strings the configurations ge nerated by this method are ambiguous, and we numerically evolve the co nfigurations forward in time to identify which regions form strings. W e find a significant rate of formation, depending on the ratio of coup lings beta. For low beta the formation rate is about one-quarter that of cosmic strings; this falls as beta is increased and above beta=1, w here the string solution is dynamically unstable, no semilocal strings form. We show the results are robust by examining different initial c onditions where, as expected in a thermal environment, the initial sca lar field need not be on the vacuum. We discuss implications for the t hree-dimensional case.