A New Twist on Spinning (A)dS Correlators

TL;DR

This paper introduces twistor space as a new framework to simplify the calculation of massless spinning correlators in cosmology, revealing their underlying simplicity and conformal properties.

Contribution

The authors develop a twistor space approach that makes conformal covariance and conservation manifest, simplifying the structure of cosmological correlators of massless spinning particles.

Findings

Twistor integrals encode conformal correlators with conservation as holomorphicity.

The twistor approach reproduces known three-point correlator results.

Half-Fourier transform connects twistor correlators to momentum space.

Abstract

Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators lies in the use of inconvenient kinematic variables. For example, in de Sitter space, consistency with unitarity and the background isometries imply that the correlators must be conformally covariant and also conserved. However, the commonly used kinematic variables for correlators do not make all of these properties manifest. In this paper, we introduce twistor space as a powerful way to satisfy all kinematic constraints. We show that conformal correlators of conserved currents can be written as twistor integrals, where the conservation condition translates into holomorphicity of the integrand. The functional form of the twistor-space correlators is very simple and easily bootstrapped. For the case of three-point functions, we verify explicitly that this reproduces known results in embedding space. We also perform a half-Fourier transform of the twistor-space correlators to obtain their counterparts in momentum space. We conclude that twistors provide a promising new avenue to study conformal correlation functions that exposes their hidden simplicity.