Line and surface defects for the free scalar field

For a single free scalar field in $d\ge 2$ dimensions, almost all the unitary conformal defects must be `trivial’ in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in $d \geq 4$andco-dimensionthreedefectsin$d \geq 5$. As an intermediate result we show that the $n$-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.