A recipe for conformal blocks
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We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group theoretic structures that depend on the quantum numbers of primary operators. These structures project into irreducible Lorentz representations. Once the Lorentz quantum numbers are accounted for there are no further calculations left to do. We compute a multivariable generalization of the Exton function. This generalized Exton function, together with the group theoretic structures, can be used to construct conformal blocks for four-point as well as higher-point correlation functions.
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Cited by 3 Pith papers
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Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS...
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Conformal Three-Point Correlation Functions from the Operator Product Expansion
A construction of embedding space three-point functions for arbitrary Lorentz representations via OPE tensor structures and group theory.
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Conformal Four-Point Correlation Functions from the Operator Product Expansion
A method is presented to derive conformal blocks for arbitrary Lorentz representations using predetermined substitutions on Gegenbauer polynomials after determining relevant group structures.
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