Conformal Three-Point Correlation Functions from the Operator Product Expansion

TL;DR

This paper develops a systematic method to construct three-point correlation functions in conformal field theories for operators in any Lorentz representation, using embedding space formalism and group theory.

Contribution

It introduces a new approach to build three-point functions directly from group theoretic objects, bypassing the operator product expansion (OPE) in conformal field theories.

Findings

Explicit construction of tensor structures for three-point functions.

Analysis of OPE coefficient properties under operator permutations.

Examples demonstrating the method's application.

Abstract

We show how to construct embedding space three-point functions for operators in arbitrary Lorentz representations by employing the formalism developed in arXiv:1905.00036 and arXiv:1905.00434. We study tensor structures that intertwine the operators with the derivatives in the OPE and examine properties of OPE coefficients under permutations of operators. Several examples are worked out in detail. We point out that the group theoretic objects used in this work can be applied directly to construct three-point functions without any reference to the OPE.