Two point functions in defect CFTs

Christopher P. Herzog, Abhay Shrestha*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
59 Downloads (Pure)


This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

Original languageEnglish
Article number226
Number of pages35
JournalJournal of High Energy Physics
Issue number4
Early online date22 Apr 2021
Publication statusPublished - Apr 2021


  • Boundary Quantum Field Theory
  • Conformal Field Theory


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