A sum rule for boundary contributions to the trace anomaly

Christopher P. Herzog, Vladimir Schaub*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in turn relates the two boundary contributions to the anomaly in the trace of the stress tensor. We check our sum rule for a variety of free theories and also for a weakly interacting theory, where a free scalar in the bulk couples marginally to a generalized free field on the boundary.

Original languageEnglish
Article number121
JournalJournal of High Energy Physics
Issue number1
Early online date21 Jan 2022
Publication statusPublished - Jan 2022


  • Anomalies in Field and String Theories
  • Boundary Quantum Field Theory
  • Conformal Field Theory


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