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

TL;DR

This paper establishes a relationship between parity-even and parity-odd correlation functions in three-dimensional conformal field theories, linking them through higher spin symmetries and implications for flat-space scattering amplitudes.

Contribution

It introduces a novel connection between parity-odd and parity-even correlators in 3D CFTs and explores their implications for higher point functions and flat-space amplitudes.

Findings

Parity-odd correlators relate to parity-even ones via higher spin symmetries.

Connection extends to higher point functions and flat-space scattering amplitudes.

Implications for non-minimal interactions like ${ ext{W}}^3$ and ${ ext{W}}^2 { ilde{ ext{W}}}$.

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