Nonholomorphic Corrections to the One-Loop N=2 Super Yang-Mills Action

In addition to the familiar contribution from a holomorphic function $\cal{F}$, the K\"ahler potential of the scalars in the nonabelian $N=2$ vector multiplet receives contributions from a real function $\cal{H}$. We determine the latter at the one-loop level, taking into account both supersymmetric matter and gauge loops. The function $\cal{H} $ characterizes the four-point coupling of the $N=2$ vector-multiplet vectors for constant values of their scalar superpartners. We discuss the consequences of our results.