A New Twist on Spinning (A)dS Correlators (2408.02727v2)

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.

• The paper introduces a twistor space method that reframes massless spinning correlators in (A)dS, streamlining the treatment of conformal symmetries.
• It simplifies complex three-point functions into compact twistor integrals, validating the approach with momentum space results.
• The study paves the way for analyzing higher-point functions and formulating recursion relations, promising improved computational techniques in cosmology.

A New Twist on Spinning (A)dS Correlators

The paper introduces an innovative approach to simplifying the analysis of massless spinning correlators in cosmology through the application of twistor space. The central thesis is that the observed complexity of cosmological correlators is a consequence of adopting suboptimal kinematic variables. Current methods in de Sitter (dS) space impose conditions of conformal covariance and conservation, which are not transparent in conventional variables. This research posits that twistor space offers a more natural framework for representing these correlators, revealing their underlying simplicity.

The authors propose that correlators in Lorentzian de Sitter space integrate naturally into the twistor formalism, where conditions of conformal symmetry and conservation are inherently satisfied. They present a methodology to express conformal correlators of conserved currents as twistor integrals, where the conservation law corresponds to the holomorphicity of the integrand. This method translates the typically intricate three-point functions into more elementary forms in twistor space, which can be corroborated with known results in embedding space.

One of the crucial demonstrations is the translation of twistor space correlators into momentum space through a half-Fourier transform, maintaining consistency with established momentum space results. This methodology indicates a potential path forward in studying higher-point functions and formulating recursion relations for cosmological correlators analogously to those in flat-space scattering amplitudes.

Key Contributions and Results:

1. Twistor Space Introduction: The paper introduces twistor space as a pertinent framework for handling massless spinning correlators in dS space. Twistor space intrinsically accommodates the symmetries and conservation laws that are considered cumbersome in conventional kinematic settings.
2. Simplification of Three-Point Functions: By utilizing this framework, the authors decompose complex three-point conformal correlators into integral forms that are straightforward and compact. This novel representation critically outmatches conventional approaches by embracing simplicity and reducing computational overhead.
3. Comparison with Momentum Space: The paper successfully derives momentum space results from twistor space representations using inverse half-Fourier transformations. This achievement corroborates twistor correlators with established momentum space correlators, confirming the validity of the twistor approach while revealing new insights into their fundamental structures.
4. Potential for Higher-Point Functions: The paper speculates on future paths for extending the twistor space methodology to higher-point cosmological correlators, offering prospects for novel insights and simplifications.

Implications and Future Directions:

The findings suggest a systematic approach to utilizing twistor space in the analysis of cosmological correlators, potentially revolutionizing our understanding of complex interactions in (Anti-)de Sitter spaces. This method holds promise for a unified representation of cosmological and particle scattering processes, where symmetries and simplifications could lead to insightful revelations on theoretical and practical levels.

Theoretical implications include better insights into the conformal field theories related to cosmological models, exposing previously hidden symmetries and relations. Practically, these advances could lead to new computational techniques that streamline the calculation of important cosmological observables.

The prospective development of twistor-based methods for higher-point functions might unlock new techniques for tackling complex cosmological scenarios, heralding advances not only in theoretical frameworks but also in precision cosmology.

This paper is a step in the exploration of twistor-based approaches that could plausibly unify our comprehension of scattering amplitudes and cosmological correlators, and it opens numerous avenues for further research, including potential exploration into an all-multiplicity formula akin to the Parke–Taylor formula for scattering amplitudes. The implications of such connections would be significant, offering new insights and techniques across the domains of theoretical physics.