  We study the contact terms that appear in the correlation functions of
exactly marginal operators using the AdS/CFT correspondence. It is known that
CFT with an exactly marginal deformation requires the existence of the contact
terms with their coefficients having a geometrical interpretation in the
context of conformal manifolds. We show that the AdS/CFT correspondence
captures properly the mathematical structure of the correlation functions that
is expected from the CFT analysis. For this purpose, we employ holographic RG
to formulate a most general setup in the bulk for describing an exactly
marginal deformation. The resultant bulk equations of motion are nonlinear and
solved perturbatively to obtain the on-shell action. We compute three- and
four-point functions of the exactly marginal operators using the GKP-Witten
prescription, and show that they match with the expected results precisely. The
cut-off surface prescription in the bulk serves as a regularization scheme for
conformal perturbation theory in the boundary CFT. As an application, we
examine a double OPE limit of the four-point functions. The anomalous
dimensions of double trace operators are written in terms of the geometrical
data of a conformal manifold.
