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.

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.