Abstract
In this paper we systematically develop the flat/CFT holographic dictionary, building on AdS/CFT holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. Our results lay foundations for further computation within the flat/celestial CFT correspondence.
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Acknowledgments
MT is supported in part by the Science and Technology Facilities Council (Consolidated Grant “Exploring the Limits of the Standard Model and Beyond”). ZH would like to thank his father Qinghe Hao and mother Xiulan Xu for providing funding for the tuition and accommodation fees when studying his PhD at the University of Southampton. ZH would also like to thank Federico Capone, Enrico Parisini and Kostas Skenderis for various discussions on celestial holography throughout the development of this work.
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Hao, Z., Taylor, M. Flat holography and celestial shockwaves. J. High Energ. Phys. 2024, 90 (2024). https://doi.org/10.1007/JHEP02(2024)090
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DOI: https://doi.org/10.1007/JHEP02(2024)090