How to get an interacting conformal line defect for free theories

A bstract We argue that interacting conformal line defects in free quantum field theories can exist, provided that inversion symmetry is broken. Important for our demonstration is the existence of a special cross ratio for bulk-defect-defect three point functions that is invariant under the conformal group but picks up a sign under inversion. We examine the particular case of a free scalar field in detail, and provide a toy model example where this bulk field interacts via a Yukawa term with fermions on the line. We expect nontrivial line defects may also exist for free Maxwell theory in four dimensions and free bulk fermions.