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

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.

Automated summary

In this study, the spinor-helicity formalism is used to calculate 3-point functions involving scalar operators and spin-s conserved currents in general 3d CFTs. It is observed that the parity-even and parity-odd parts of a correlator are related in spinor-helicity variables. After converting spinor-helicity answers to momentum space, correlators involving spin-s currents can be expressed in terms of simple conformally invariant conserved structures, allowing for systematic understanding and separation of contact terms, particularly for the parity-odd case. Additionally, some of the correlators are reproduced using weight-shifting operators.