Conformal Contact Terms and Semi-local Terms

We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables, but they do appear in physically important correlation functions such as (anomalous) Ward–Takahashi identities or Schwinger–Dyson equations. We develop some tools such as embedding space delta functions and effective action to examine conformal invariance of these local terms.