# A recipe for conformal blocks

## TL;DR

This paper presents a systematic method for constructing conformal blocks in any dimension, simplifying calculations to group theory structures and providing a generalized Exton function for multi-point functions.

## Contribution

It introduces a universal prescription for conformal blocks that reduces the problem to group theory and provides a new multivariable Exton function for higher-point correlators.

## Key findings

- Explicit construction of conformal blocks in arbitrary dimensions
- Introduction of a generalized Exton function for multivariable cases
- Simplification of conformal block calculations to group theoretic methods

## Abstract

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.