Small-instanton transitions in F-theory

We study the phase transition between G-instantons and D3-branes quantitatively. A G-instanton is a classical solution to the self-dual equation of the M/F-theory three-form tensor field C in the complex fourfold. This phase transition is dual to that between 'vertical' small instantons and 5-branes in the heterotic string. Using G as a background gauge flux, we may dynamically control the gauge symmetry breaking and connect between different vacua of F-theory. We may understand the amount of flux undergoing the phase transition and the resulting number of D3-branes in terms of group-theoretical quantities. We also discuss the resulting chirality change and preservation of anomaly freedom.