The Effective K\"ahler Potential And Extra Space-Time Dimensions

The effects of extra space-time dimensions on the Wilsonian effective K\"ahler potential and the perturbative one loop effective K\"ahler potential are determined within the framework of an Abelian gauge theory with N=2 supersymmetric field content. The relation between the K\"ahler metric and the effective gauge couplings which leads to the absence of radiative corrections to the K\"ahler potential is expressed as a function of the radius of compactification of a fifth dimension. In general, the quantum corrections to the low energy K\"ahler potential are shown to grow with this radius reflecting the underlying higher dimensional nature of the theory.