Pergola, Paolo Spinning Celestial Correlators: from Propagators to Higher Point Functions. [Tesi di dottorato]

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Abstract

Anti-de Sitter/Conformal field theory (AdS/CFT) correspondence is one of the best-understood realisations of the holographic principle in quantum gravity. A central open problem is the extension of this holographic correspondence to the other maximally symmetric spacetimes with zero and positive cosmological constant, namely Minkowski and de Sitter (dS) space, as they are relevant for the description of our universe on galactic and cosmological scales. In Minkowski space, one of the most recent approaches is celestial holography. This framework conjectures a duality between theories defined in Minkowski space and putative CFTs living on a codimension-two boundary, the so-called celestial sphere. Recently, a novel off-shell approach has been introduced in the literature, which proposes to extrapolate correlators on the celestial sphere starting from the corresponding time-ordered correlators in Minkowski. The corresponding correlation functions on the celestial sphere have been named celestial correlators. In this thesis we focus on this off-shell approach to celestial holography and we investigate how to generalize it to the case of spinning fields. The main contributions presented in this work can be divided into two main parts. In the first part of this thesis, we consider the radial reduction of propagators in the hyperbolic foliation of Minkowski space. We study in detail the Euclidean version of this problem, showing how the scalar and spin-1 propagators can be radially reduced on spheres in terms of spherical harmonics. From this decomposition we obtain the corresponding radial reduction in Minkowski via analytic continuation and Watson-Sommerfeld transform. For the second part, we introduce the Mellin amplitudes representation of celestial correlators. We compute the corresponding Mellin amplitudes for various diagrams with external scalar operators. Starting from the scalar contact diagrams and exchanges, we then consider the case of spinning exchange, deriving results for generic spin. We show how to extract operator product expansion (OPE) data from the Mellin amplitudes of exchange diagrams and how to identify the family of conformal operators dual to the field exchanged in the bulk. We also test the celestial OPE for the case of scalar fields.

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