Relation between parity-even and parity-odd CFT correlation functions in three dimensions

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 W3 and W2W~. In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.