  We analyze the coupled N=2 supergravity and Yang-Mills system using
holomorphy, near the rigid limit where the former decouples from the latter. We
find that there appears generically a new mass scale around g M_{pl} where g is
the gauge coupling constant and M_{pl} is the Planck scale. This is in accord
with the weak-gravity conjecture proposed recently. We also study the scale
dependence of the gauge theory prepotential from its embedding into
supergravity.
