  We study the effects of extra spacetime dimensions at intermediate mass
scales, as expected in string theories with large-radius compactifications, and
focus on the gauge and Yukawa couplings within the Minimal Supersymmetric
Standard Model. We find that extra spacetime dimensions naturally lead to the
appearance of grand unified theories at scales substantially below the usual
GUT scale. Furthermore, we show that extra spacetime dimensions provide a
natural mechanism for explaining the fermion mass hierarchy by permitting the
Yukawa couplings to receive power-law corrections. We also discuss how
proton-decay constraints may be addressed in this scenario, and suggest that
proton-decay amplitudes may be exactly cancelled to all orders in perturbation
theory as a result of new Kaluza-Klein selection rules corresponding to the
extra spacetime dimensions.
