  Celestial amplitudes obtained from Mellin transforming 4d momentum space
scattering amplitudes contain distributional delta functions, hindering the
application of conventional CFT techniques. In this paper, we propose to bypass
this problem by recognizing Mellin transforms as integral transforms
projectivizing certain components of the angular momentum. It turns out that
the Mellin transformed wavefunctions in the conformal primary basis can be
regarded as representatives of certain cohomology classes on the minitwistor
space of the hyperbolic slices of 4d Minkowski space. Geometrically, this
amounts to treating 4d Minkowski space as the embedding space of AdS3. By
considering scattering of such on-shell wavefunctions on the projective spinor
bundle PS of Euclidean AdS3, we bypass the difficulty of the distributional
properties of celestial correlators using the traditional AdS3/CFT2 dictionary
and find conventional 2d CFT correlators for the scaling reduced Yang-Mills
theory living on the hyperbolic slices. In the meantime, however, one is
required to consider action functionals on the auxiliary space PS, which
introduces additional difficulties. Here we provide a framework to work on the
projective spinor bundle of hyperbolic slices, obtained from a careful scaling
reduction of the twistor space of 4d Minkowski spacetime.
