Recursion relation for general 3d blocks
Rajeev Erramilli (Department of Physics, Yale University, New Haven, CT, 06520, USA); Luca Iliesiu (Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA); Petr Kravchuk (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA)
We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin (d) are known.
