General Bootstrap Equations in 4D CFTs

TL;DR

This paper introduces a unified framework for 4D conformal bootstrap computations, combining covariant and non-covariant formalisms, with practical tools like a Mathematica package for researchers.

Contribution

It unifies two approaches to 4D conformal bootstrap, providing explicit constructions and a software implementation for broader accessibility.

Findings

Unified formalism for tensor structures and differential operators

Explicit classification of n-point tensor structures

Implementation of a Mathematica package for bootstrap computations

Abstract

We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of n-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Finally, we implement our framework in a Mathematica package and make it freely available.