  We study the effect of marginal and irrelevant deformations on the
renormalization of operators near a CFT fixed point. New divergences in a given
operator are determined by its OPE with the operator D that generates the
deformation. This provides a scheme to compute the couplings a_DAB between the
operator D and two arbitrary operators O_A and O_B. We exemplify for the case
of N=4 SYM, considering the simplest case of the exact Lagrangian deformation.
In this case the deformed anomalous dimension matrix is determined by the
derivative of the anomalous dimension matrix with respect to the coupling. We
use integrability techniques to compute the one-loop couplings a_LAB between
the Lagrangian and two distinct large operators built with Magnons, in the
SU(2) sector of the theory. Then we consider a_DAA at strong coupling, and show
how to compute it using the gauge/gravity duality, when D is a chiral operator
dual to any supergravity field and O_A is dual to a heavy string state. We
exemplify for the Lagrangian and operators O_A dual to heavy string states,
showing agreement with the prediction derived from the renormalization group
arguments.
