Celestial Holography Revisited

Abstract

We revisit the prescription commonly used to define holographic correlators on the celestial sphere of Minkowski space as an integral transform of flat space scattering amplitudes, known as celestial amplitudes. We propose a resolution to a discrepancy noted in the computation of celestial amplitudes, which arises from the regularisation and the commutation of a divergent integral in the definition of conformal primary wave functions. Motivated by this, we propose a novel, off-shell, prescription for holographic correlators on the celestial sphere which we refer to as celestial correlators. The latter are defined by the Mellin transform of bulk time-ordered correlators with respect to the radial direction in the hyperbolic slicing of Minkowski space, which are then extrapolated to the celestial sphere along the hyperbolic directions. This prescription is analogous to the extrapolate definition of holographic correlators in AdS/CFT and, like in AdS, is centered on (off-shell) correlation functions as opposed to (on-shell) S-matrix elements. We show that celestial correlators defined in this new way are manifestly recast in terms of corresponding Witten diagrams in Euclidean anti-de Sitter space in perturbation theory. We discuss the possibility of using this definition of celestial correlators in terms of bulk correlation functions to explore the non-perturbative properties of celestial correlators dual to conformal field theories in Minkowski space. We furthermore show that celestial amplitudes can also be defined by a similar extrapolation of S-matrices in position space via a Mellin transformation in the radial direction. This provides the proper regularisation of conformal primary wave functions, which is inherited from the corresponding Wightman functions.