Conformal Bootstrap in Embedding Space

TL;DR

This paper presents a method to derive conformal blocks directly in embedding space using the operator product expansion, enabling an analytic conformal bootstrap approach with a Jacobi-like framework.

Contribution

It introduces a way to obtain all conformal blocks from a minimal scalar exchange in embedding space, simplifying the analytic bootstrap process.

Findings

Conformal blocks can be derived from scalar exchange in embedding space.

All conformal blocks are derivatives of the minimal scalar block.

Analytic bootstrap can be implemented directly in embedding space.

Abstract

It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All remaining conformal blocks are simple derivatives of the minimal conformal block. With the help of the orthogonality properties of the conformal blocks, the analytic conformal bootstrap can be implemented directly in embedding space, leading to a Jacobi-like definition of conformal field theories.