Conformal Two-Point Correlation Functions from the Operator Product Expansion

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.

1+26 pages

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• The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field
• All Global One- and Two-Dimensional Higher-Point Conformal Blocks