Celestial holography and AdS 3/CFT 2 from a scaling reduction of twistor space

Abstract

Abstract 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 AdS 3. By considering scattering of such on-shell wavefunctions on the projective spinor bundle ℙ𝕊 of Euclidean AdS 3, we bypass the difficulty of the distributional properties of celestial correlators using the traditional AdS 3 /CFT 2 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.

Keywords

• Scattering Amplitudes
• AdS-CFT Correspondence
• Conformal and W Symmetry
• Field Theories in Lower Dimensions