From AdS Propagators to Celestial Propagators

TL;DR

This paper explores how AdS scalar propagators can be expressed in the celestial basis, revealing structural similarities and differences for massless and massive fields, and connecting AdS and celestial holography.

Contribution

It provides a detailed translation of AdS scalar propagators into the celestial basis using conformal primary wavefunctions for both massless and massive cases.

Findings

Massless celestial propagator reduces to a 2D boundary object on the celestial sphere.

Massive celestial propagator involves modified Bessel functions, resembling AdS radial structure.

Structural translation links AdS propagators with celestial propagators.

Abstract

In this paper, we investigate how AdS scalar propagators are represented in the celestial basis. Starting from the standard bulk-to-boundary propagator in Euclidean AdS space, we express the propagator in a Schwinger parametrization and construct the corresponding boundary-to-boundary propagator. We then transform the resulting propagators to the celestial basis using conformal primary wavefunctions for both massless and massive scalar fields. For the massless case, the celestial propagator reduces to an effectively two-dimensional boundary-to-boundary object on the celestial sphere dependent on the AdS/CFT conformal dimension $\Delta$. For the massive case, the celestial propagator exhibits a nontrivial kernel involving modified Bessel functions, closely resembling the momentum-space radial structure of AdS bulk-to-boundary propagators. The results suggest a structural translation from AdS propagators and celestial propagators.