  If the AdS/CFT correspondence is valid in the Coulomb branch, the potential
between waves on a pair of test branes in the bulk should be reproduced by the
relevant Yang-Mills theory effective action on the boundary. Earlier work has
provided evidence for this in the case of constant gauge field brane waves. In
this paper we provide concrete evidence for an earlier proposal that the
effects of exchange of supergravity modes with nonzero momentum in the brane
directions are encoded in certain terms involving derivatives of the field
strength in the gauge theory effective action. We explicitly calculate the
force quadratic in the field strengths coming from the exchange of non-zero
momentum two form fields between two 3-branes in $AdS_5 \times S^5$ to lowest
nontrivial order in the momentum. We show that this is exactly the same as that
between the branes living in flat space. The result is in agreement with the
gauge theory effective action and consistent with the non-renormalization
property of this term. We comment on the relationship of other ``acceleration''
terms in the SYM effective action with quantities in supergravity.
