  We discuss consequences of the breaking of conformal symmetry by a flat or
spherical extended operator. We adapt the embedding formalism to the study of
correlation functions of symmetric traceless tensors in the presence of the
defect. Two-point functions of a bulk and a defect primary are fixed by
conformal invariance up to a set of OPE coefficients, and we identify the
allowed tensor structures. A correlator of two bulk primaries depends on two
cross-ratios, and we study its conformal block decomposition in the case of
external scalars. The Casimir equation in the defect channel reduces to a
hypergeometric equation, while the bulk channel blocks are recursively
determined in the light-cone limit. In the special case of a defect of
codimension two, we map the Casimir equation in the bulk channel to the one of
a four-point function without defect. Finally, we analyze the contact terms of
the stress-tensor with the extended operator, and we deduce constraints on the
CFT data. In two dimensions, we relate the displacement operator, which appears
among the contact terms, to the reflection coefficient of a conformal
interface, and we find unitarity bounds for the latter.
