  Known examples of unitary relativistic scale but not conformal-invariant
field theories (SFTs) can be embedded into conventional conformal field
theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is
a free theory. Our discussion applies to an arbitrary number of spacetime
dimensions and explains triviality of known SFTs in four spacetime dimensions.
We comment on examples of unitary SFTs which are not captured by our
construction.

High Energy Physics - Theory