Relation between parity-even and parity-odd CFT correlation functions in three dimensions
Sachin Jain, Renjan Rajan John
Abstract
A bstract 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 $$ {\mathcal{W}}^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> and $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mover> <mml:mi>W</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> </mml:math> . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.