  We study the operator product expansion (OPE) for scalar conformal defects of
any codimension in CFT. The OPE for defects is decomposed into "defect OPE
blocks", the irreducible representations of the conformal group, each of which
packages the contribution from a primary operator and its descendants. We use
the shadow formalism to deduce an integral representation of the defect OPE
blocks. They are shown to obey a set of constraint equations that can be
regarded as equations of motion for a scalar field propagating on the moduli
space of the defects. By employing the Radon transform between the AdS space
and the moduli space, we obtain a formula of constructing an AdS scalar field
from the defect OPE block for a conformal defect of any codimension in a scalar
representation of the conformal group, which turns out to be the Euclidean
version of the HKLL formula. We also introduce a duality between conformal
defects of different codimensions and prove the equivalence between the defect
OPE block for codimension-two defects and the OPE block for a pair of local
operators.
