# On conformal correlators and blocks with spinors in general dimensions

## TL;DR

This paper develops a method to compute conformal correlation functions involving spinors, tensors, and their combinations in any dimension, using the embedding space formalism and differential operators to simplify the derivation of conformal blocks.

## Contribution

It introduces a systematic approach to derive conformal blocks with spinor fields in general dimensions, extending previous scalar-focused methods.

## Key findings

- Derived explicit forms of three-point functions with spinor fields.
- Expressed four-point conformal blocks with spinors in terms of scalar blocks and differential operators.
- Facilitated the computation of geodesic Witten diagrams for spinor correlators.

## Abstract

We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For this, the embedding space formalism is employed and the polarisation spinors are introduced to simplify the computations. Three-point functions are rewritten in terms of differential operators acting on scalar-scalar-tensor correlation functions. This enables us to determine conformal blocks for four-point functions with scalar and spinor fields by acting the differential operators on scalar conformal blocks, which will be useful in finding their geodesic Witten diagrams.