Deconstructing Conformal Blocks in 4D CFT

TL;DR

This paper develops a method to relate and compute conformal blocks in 4D CFTs using differential operators, simplifying the bootstrap process for tensor correlators.

Contribution

It introduces explicit differential operators for all conformal partial waves of traceless symmetric operators in 4D CFTs, enabling efficient extraction from seed correlators.

Findings

Explicit differential operators constructed for all tensor conformal blocks.

Simplified computation of tensor conformal blocks from seed correlators.

Enhanced tools for conformal bootstrap in four-dimensional theories.

Abstract

We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few "seed" correlators, simplifying dramatically the computation needed to bootstrap tensor correlators.