Ward identities connect bulk and defect correlators

What the study found: The authors derive integral identities that relate correlation functions involving bulk and defect operators, including tilt operators, to lower-point bulk-defect correlators. These identities are based on an analysis of the Lie algebra of the symmetry group before and after defect-induced symmetry breaking.

Why the authors say this matters: The authors conclude that these identities are a useful tool for checking existing perturbative correlators and for imposing nontrivial constraints on conformal field theory (CFT) data, where CFT means a theory with conformal symmetry.

What the researchers tested: The paper studies conformal field theory with defects, where a defect can break a global symmetry and produce defect operators. The authors derive Ward-identity-based integral relations and illustrate them with the 1/2 BPS Maldacena-Wilson loop in N=4 super Yang-Mills theory and with magnetic lines in the O(N) model in 4 minus epsilon dimensions.

What worked and what didn't: The identities are shown to relate bulk and defect correlators to lower-point bulk-defect correlators. The authors also demonstrate that these relations can check existing perturbative correlators and constrain CFT data. The abstract does not report any failed cases.

What to keep in mind: The available summary does not describe detailed limitations, and the examples are restricted to the two settings named in the abstract.

Key points

• The authors derive integral identities linking bulk and defect correlation functions, including those involving tilt operators.
• The identities are based on symmetry analysis before and after defect-induced symmetry breaking.
• The paper illustrates the method with the 1/2 BPS Maldacena-Wilson loop in N=4 super Yang-Mills theory and magnetic lines in the O(N) model in 4 minus epsilon dimensions.
• The authors say the identities can check perturbative correlators and constrain conformal field theory data.
• The abstract does not describe detailed limitations or failed cases.