Abstract
In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as {mathcal{W}}^3 and {mathcal{W}}^2tilde{mathcal{W}} . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.
Highlights
AdS4 × S7 [8, 9]
It was shown in [47], that correlation functions in spinor-helicity variables in Chern-Simons matter theories can be written down using either free fermionic or free bosonic results. This poses the question, if this relation is special to spinor-helicity variables, or can one find out such relations in position space and momentum space as well? The aim of this note is to write down a precise relation between the parity-even and the parity-odd contributions to a correlator in position and momentum space
This relation in particular would imply that the parity-odd part of the correlation function of conserved currents can be obtained from free theory
Summary
We collect the orthogonal projectors that will be useful in the subsequent sections. We use the following parity-even projector to project spin-1 conserved currents πμν (k). For spin-2 conserved currents, projectors are defined such that they are orthogonal and traceless. The parity-even and parity-odd projectors in this case are given by. A relation between even and odd projectors. We observe the following relations between the parity-even and the parity-odd projectors defined above. For the spin-1 case, we have 1 k μαkπαν (k) = χμν (k),. It is convenient to state these relations in terms of transverse, null polarization vectors which satisfy ki · zi = 0 and zi2 = 0. Takes the parity-even projector to the parity-odd projector
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