Line and surface defects for the free scalar field

A bstract For a single free scalar field in d ≥ 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 ≥ 4 and co-dimension three defects in d ≥ 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.