The dynamics of small instanton phase transitions

The small instanton transition of a five-brane colliding with one end of theS1/Z2 interval in heterotic M-theory is discussed, with emphasis on thetransition moduli, their potential function and the associated non-perturbativesuperpotential. Using numerical methods, the equations of motion of thesemoduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solvedincluding non-perturbative interactions. It is shown that the five-branecollides with the end of the interval at a small instanton. However, the modulithen continue to evolve to an isolated minimum of the potential, where they aretrapped by gravitational damping. The torsion free sheaf at the small instantonis ``smoothed out'' into a vector bundle at the isolated minimum, thusdynamically completing the small instanton phase transition. Radiative dampingat the origin of moduli space is discussed and shown to be insufficient to trapthe moduli at the small instanton point.Comment: LaTeX, 23 pages, 7 figures; minor corrections, references adde