Partial wave expansion and Wightman positivity in conformal field theory

TL;DR

This paper introduces a new method for exact conformal partial wave expansions to analyze Hilbert space positivity in a non-perturbative 4D conformal field theory model, leveraging bilocal fields and harmonic decomposition.

Contribution

It develops a novel approach for computing conformal partial wave expansions and applies it to study Wightman positivity in a non-perturbative 4D model with global conformal invariance.

Findings

New method for exact conformal partial wave expansion

Application to Hilbert space positivity in 4D CFT

Analysis of scalar field contributions in 6-point functions

Abstract

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based on the assumption of global conformal invariance on compactified Minkowski space. Bilocal fields arising in the harmonic decomposition of the operator product expansion prove to be a powerful instrument in exploring the field content. In particular, in the theory of a field of dimension 4 which has the properties of a (gauge invariant) Lagrangian, the scalar field contribution to the 6-point function of the twist 2 bilocal field is analyzed with the aim to separate the free field part from the nontrivial part.