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

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Bu, Wei 
Seet, Sean 


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.


Acknowledgements: It is a pleasure to thank Tim Adamo and David Skinner for discussions. We also thank Tim Adamo, Simon Heuveline and David Skinner for commenting on earlier versions of the draft. A large amount of the twistor theory (including all sections without citations to extant work) is due to many productive discussions and original work by SS with Yvonne Geyer, Lionel Mason and especially David Skinner about the corresponding story in AdS5, minimally adapted to the AdS3 case. WB is supported by the Royal Society Studentship. SS is supported by the Trinity College Internal Graduate Studentship. The work of SS has been supported in part by STFC consolidated grants ST/T000694/1 and ST/X000664/1.


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

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Journal of High Energy Physics

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Springer Berlin Heidelberg