How to get an interacting conformal line defect for free theories

Abstract

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.

arXiv comment31 pages, 6 figures. v2: clarified some technical details, and some updated references. v3: addressed suggestions by referee. v4: further suggestions by referee