# Conformal Contact Terms and Semi-Local Terms

## TL;DR

This paper investigates the conformal invariance of local contact and semi-local terms in correlation functions of conformal field theories, developing new tools to analyze their properties and significance.

## Contribution

It introduces methods like embedding space delta functions and effective actions to study the conformal properties of local terms in correlation functions.

## Key findings

- Not all local terms are universal observables.
- Local terms appear in important physical identities like Ward-Takahashi and Schwinger-Dynson equations.
- Developed tools to examine conformal invariance of contact and semi-local terms.

## Abstract

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-Dynson equations. We develop some tools such as embedding space delta functions and effective action to examine conformal invariance of these local terms.