Spinning Conformal Blocks

TL;DR

This paper presents a new method using embedding space formalism to derive conformal blocks involving traceless symmetric tensors in any dimension, simplifying calculations especially in three-dimensional conformal field theories.

Contribution

It introduces a differential operator approach to generate conformal blocks for operators with spin, extending the ability to compute these blocks in arbitrary dimensions.

Findings

All conformal blocks in three dimensions can be expressed using this method.

The approach simplifies calculations of conformal blocks involving spinning operators.

Demonstrated applications in simple examples show the method's effectiveness.

Abstract

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.