Spinors and conformal correlators

TL;DR

This paper develops a formalism using spinors to parameterize 2- and 3-point functions in 3D conformal field theory, simplifying the operator product expansion and revealing unitarity constraints.

Contribution

It introduces a novel spinor-based parameterization for 3-point functions in 3D conformal field theory, extending known 2-point function techniques.

Findings

Simplifies the expression of 3-point functions using spinors.

Provides a clear realization of the operator product expansion in 3D.

Exposes implications of unitarity in the helicity basis.

Abstract

In conformal field theory, momentum eigenstates can be parameterized by a pair of real spinors, in terms of which special conformal transformations take a simpler form. This well-known fact allows to express 2-point functions of primary operators in the helicity basis, exposing the consequences of unitarity. What is less known is that the same pair of spinors can be used, together with a pair of scalar quantities, to parameterize 3-point functions. We develop this formalism in 3 dimensions and show that it provides a simple realization of the operator product expansion (OPE) for scalar primary operators acting on the vacuum.