  Coupling constants at high energy scales are studied in SU(N) gauge theory
with distinct sizes of extra dimensions. We present the solution of gauge
couplings as functions of the energy in such a way as to track the number of
Kaluza-Klein modes. In a flat extra dimension, it is shown that the gauge
couplings have logarithmic dependence on the size of the extra dimension and
linear dependence on the number of Kaluza-Klein modes. We find some patterns of
the dependence on flavor of bulk and brane fermions. Dependence of gauge
couplings on the size of an extra dimension is discussed also in a warped extra
dimension.
