Higher spin 3-point functions in 3d CFT using spinor-helicity variables

TL;DR

This paper employs spinor-helicity variables to compute 3-point functions involving scalar operators and conserved currents in 3d CFTs, revealing relations between parity-even and parity-odd parts and providing systematic contact term separation.

Contribution

It introduces a novel application of spinor-helicity formalism to 3d CFT correlators, enabling simplified expressions and contact term analysis, including parity-odd structures.

Findings

Correlators expressed in simple conformally invariant structures.

Parity-even and parity-odd parts are related in spinor-helicity variables.

Systematic separation of contact terms achieved, especially for parity-odd cases.

Abstract

In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-$s$ conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-$s$ currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.