Non-Standard Fermion Propagators from Conformal Field Theory

TL;DR

This paper connects 4D fermion propagators with conformal field theory by expressing Weyl spinors as primary fields, leading to a new understanding of their Lorentz covariant correlators and symmetry properties.

Contribution

It introduces a novel conformal field theory framework for analyzing fermion propagators in four-dimensional spacetime, revealing their structure and symmetry constraints.

Findings

Fermion two-point functions can be expressed via primary field correlators.

Chiral symmetry breaking terms resemble 2D CFT fermionic correlators.

Framework enables covariant meromorphy constraints on 4D spinors.

Abstract

It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. I employ this observation to determine the general structure of the corresponding Lorentz covariant correlators by methods similar to the methods employed in conformal field theory to determine 2- and 3-point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic 2-point functions of 2D CFT up to a function of the product of momenta. The construction also permits for the formulation of covariant meromorphy constraints on spinors in 3+1 dimensions.