Recursion relation for general 3d blocks

Understand

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.