Locality, bulk equations of motion and the conformal bootstrap

Understand

We develop an approach to construct local bulk operators in a CFT to order $1/N^2$.

• Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator.
• Using previous results on 3-point functions we construct a local bulk operator in each OPE channel.
• We then impose the condition that the bulk operators constructed in different channels agree, and hence give rise to a well-defined bulk operator.