Defect a-theorem and a-maximization

Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to, and generalize those of standalone CFTs. Here we study the conformal a- and c-anomalies of four dimensional defects in CFTs of general spacetime dimensions greater than four. We prove that under unitary defect renormalization group (RG) flows, the defect a-anomaly must decrease, thus establishing the defect a-theorem. For conformal defects preserving minimal supersymmetry, the full defect symmetry contains a distinguished U(1)(R) subgroup. We derive the anomaly multiplet relations that express the defect a- and c-anomalies in terms of the defect (mixed) 't Hooft anomalies for this U(1)(R) symmetry. Once the U(1)(R) symmetry is identified using the defect a-maximization principle which we prove, this enables a nonperturbative pathway to the conformal anomalies of strongly coupled defects. We illustrate our methods by discussing a number of examples including boundaries in five dimensions and codimension-two defects in six dimensions. We also comment on chiral algebra sectors of defect operator algebras and potential conformal collider bounds on defect anomalies.

Automated summary

This paper studies the universal behaviors of a CFT in the presence of defects, proving that the defect a-anomaly must decrease under unitary defect RG flows and deriving the relation between the defect a- and c-anomalies and the U(1)(R) symmetry anomalies. The methods are illustrated with examples and the potential collider bounds on defect anomalies are discussed.