  We give an effective field theory derivation, based on the running of Planck
brane gauge correlators, of the large logarithms that arise in the predictions
for low energy gauge couplings in compactified AdS}_5 backgrounds, including
the one-loop effects of bulk scalars, fermions, and gauge bosons. In contrast
to the case of charged scalars coupled to Abelian gauge fields that has been
considered previously in the literature, the one-loop corrections are not
dominated by a single 4D Kaluza-Klein mode. Nevertheless, in the case of gauge
field loops, the amplitudes can be reorganized into a leading logarithmic
contribution that is identical to the running in 4D non-Abelian gauge theory,
and a term which is not logarithmically enhanced and is analogous to a two-loop
effect in 4D. In a warped GUT model broken by the Higgs mechanism in the
bulk,we show that the matching scale that appears in the large logarithms
induced by the non-Abelian gauge fields is m_{XY}^2/k where m_{XY} is the bulk
mass of the XY bosons and k is the AdS curvature. This is in contrast to the UV
scale in the logarithmic contributions of scalars, which is simply the bulk
mass m. Our results are summarized in a set of simple rules that can be applied
to compute the leading logarithmic predictions for coupling constant relations
within a given warped GUT model. We present results for both bulk Higgs and
boundary breaking of the GUT gauge group.
