Celestial Holography Revisited II: Correlators and Källén-Lehmann
arxiv(2024)
摘要
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
Källén-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.
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