The Dynamics of Small Instanton Phase Transitions

TL;DR

This paper investigates the dynamics of small instanton phase transitions in heterotic M-theory, demonstrating how moduli evolve and become trapped in a potential minimum after a five-brane collision, completing the transition.

Contribution

It provides a detailed numerical analysis of moduli evolution during small instanton transitions, including non-perturbative effects and gravitational damping mechanisms.

Findings

Five-brane collision leads to moduli being trapped at a potential minimum.

Moduli continue to evolve and are smoothed into a vector bundle after the transition.

Radiative damping alone is insufficient to trap the moduli at the small instanton point.

Abstract

The small instanton transition of a five-brane colliding with one end of the S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the transition moduli, their potential function and the associated non-perturbative superpotential. Using numerical methods, the equations of motion of these moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved including non-perturbative interactions. It is shown that the five-brane collides with the end of the interval at a small instanton. However, the moduli then continue to evolve to an isolated minimum of the potential, where they are trapped by gravitational damping. The torsion free sheaf at the small instanton is ``smoothed out'' into a vector bundle at the isolated minimum, thus dynamically completing the small instanton phase transition. Radiative damping at the origin of moduli space is discussed and shown to be insufficient to trap the moduli at the small instanton point.