# Conformal Two-Point Correlation Functions from the Operator Product Expansion

## TL;DR

This paper derives the most general conformal two-point functions in arbitrary Lorentz representations using the embedding space formalism, providing explicit examples and constraints on OPE coefficients to ensure unitarity.

## Contribution

It applies the embedding space formalism to compute general two-point functions in arbitrary Lorentz representations and derives unitarity constraints on OPE coefficients.

## Key findings

- Explicit general two-point functions in embedding space for any Lorentz representation.
- Consistency with conformal covariance upon projection to position space.
- Unitarity constraints on OPE coefficient matrices.

## Abstract

We compute the most general embedding space two-point function in arbitrary Lorentz representations in the context of the recently introduced formalism in arXiv:1905.00036 and arXiv:1905.00434. This work provides a first explicit application of this approach and furnishes a number of checks of the formalism. We project the general embedding space two-point function to position space and find a form consistent with conformal covariance. Several concrete examples are worked out in detail. We also derive constraints on the OPE coefficient matrices appearing in the two-point function, which allow us to impose unitarity conditions on the two-point function coefficients for operators in any Lorentz representations.

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Source: https://tomesphere.com/paper/1906.12349