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

Abstract

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 W 3 $$ {\mathcal{W}}^3 $$ and W 2 W ˜ $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

Keywords

• Conformal Field Theory
• Chern-Simons Theories