Celestial Holography Revisited II: Correlators and K\"all\'en-Lehmann

TL;DR

This paper advances celestial holography by establishing Feynman rules for correlators, proving their relation to EAdS Witten diagrams, and exploring non-perturbative spectral properties of scalar two-point functions.

Contribution

It provides a complete set of Feynman rules for celestial correlators, proves their equivalence to EAdS Witten diagrams, and investigates non-perturbative spectral features.

Findings

Celestial correlators can be expressed as EAdS Witten diagrams.

The radial reduction of the K"allén-Lehmann spectral representation is derived.

The spectral function is meromorphic and connected to the Watson-Sommerfeld transform.

Abstract

In this work we continue the investigation of the extrapolate dictionary for celestial holography recently proposed in [2301.01810], at both the perturbative and non-perturbative level. Focusing on scalar field theories, we give a complete set of Feynman rules for extrapolate celestial correlation functions and their radial reduction in the hyperbolic slicing of Minkowski space. We prove to all orders in perturbation theory that celestial correlators can be re-written in terms of corresponding Witten diagrams in EAdS which, in the hyperbolic slicing of Minkowski space, follows from the fact that the same is true in dS space. We then initiate the study of non-perturbative properties of celestial correlators, deriving the radial reduction of the K\"all\'en-Lehmann spectral representation of the exact Minkowski two-point function. We discuss the analytic properties of the radially reduced spectral function, which is a meromorphic function of the spectral parameter, and highlight a connection with the Watson-Sommerfeld transform.