Krasnov And

We use AdS/CFT inspired methods to study the Lorentz group SO(1, d + 1) Racah coefficients for type I representations. For such representations the Racah coefficient can be represented as an integral of a product of 6 bulk-to-bulk propagators over 4 copies of the hyperbolic space Hd+1. To compute the integrals we represent the bulk-to-bulk propagators in terms of bulk-to-boundary ones. The bulk integrals can be computed explicitly, and the boundary integrations are carried out by introducing Feynman parameters. The final result is an integral representation of the Racah coefficient given by 4 Barnes-Mellin type integrals.