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

Implications of the AdS/CFT Correspondence on Spacetime and Worldsheet OPE Coefficients