Spinors and conformal correlators

Abstract

In conformal field theory, momentum eigenstates can be parameterized by a pair of real spinors, in terms of which special conformal transformations take a simpler form. This well-known fact allows to express 2-point functions of primary operators in the helicity basis, exposing the consequences of unitarity. What is less known is that the same pair of spinors can be used, together with a pair of scalar quantities, to parameterize 3-point functions. We develop this formalism in 3 dimensions and show that it provides a simple realization of the operator product expansion (OPE) for scalar primary operators acting on the vacuum.

22 + 11 pages, one figure. v2: matches published version

References in corpus (15)

• Spinning AdS Propagators
• Comments on Unparticles
• Analyticity and Unitarity for Cosmological Correlators
• From dS to AdS and back
• Lightcone Bootstrap at higher points
• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Distributions in CFT II. Minkowski Space
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• Tensors and Spinors in de Sitter Space
• $\lambda {\varphi }^4$ in dS
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Conformal partial waves in momentum space
• Conformal-helicity duality & the Hilbert space of free CFTs
• From Schwinger to Wightman: all conformal 3-point functions in momentum space