  We provide evidence for the validity of AdS/CFT correspondence in the Coulomb
branch by comparing the Yang-Mills effective action with the potential between
waves on two separated test 3-branes in the presence of a large number of other
3-branes. For constant gauge fields excited on the branes, this requires that
the supergravity potential in a $AdS_5 \times S^5$ background is the {\it same}
as that in flat space, despite the fact that both propagators and couplings of
some relevant supergravity modes are different. We show that this is indeed
true, due to a subtle cancellation. With time-dependent gauge fields on the
test branes, the potential is sensitive to retardation effects of causal
propagation in the bulk. We argue that this is reflected in higher derivative
(acceleration) terms in the Yang-Mills effective action. We show that for two
3-branes separated in flat space the structure of lowest order acceleration
terms is in agreement with supergravity expectations.

High Energy Physics - Theory;General Relativity and Quantum Cosmology