  We explore the connection between the operator product expansion (OPE) in the
boundary and worldsheet conformal field theories in the context of
AdS$_{d+1}$/CFT$_d$ correspondence. Considering single trace scalar operators
in the boundary theory and using the saddle point analysis of the worldsheet
OPE [1], we derive an explicit relation between OPE coefficients in the
boundary and worldsheet theories for the contribution of single trace spin
$\ell$ operators to the OPE. We also consider external vector operators and
obtain the relation between OPE coefficients for the exchange of single trace
scalar operators in the OPE. We revisit the relationship between the bulk cubic
couplings in the Supergravity approximation and the OPE coefficients in the
dual boundary theory. Our results match with the known examples from the case
of AdS$_3$/CFT$_2$. For the operators whose two and three point correlators
enjoy a non renormalization theorem, this gives a set of three way relations
between the bulk cubic couplings in supergravity and the OPE coefficients in
the boundary and worldsheet theories.
