A Recipe for Conformal Blocks

  • Witold Skiba Department of Physics, Yale University, New Haven, CT 06520, USA https://orcid.org/0000-0002-2800-4148
  • Jean-Francois Fortin Departement de Physique, de Genie Physique et d’Optique, Universite Laval, Quebec, QC G1V 0A6, Canada
Keywords: conformal field theories, conformal blocks


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.