Abstract
In this note we determine the graviton-graviton OPE and the null states in any w1+∞ symmetric theory on the celestial sphere. Our analysis shows that there exists a discrete infinite family of such theories. The MHV-sector and the quantum self dual gravity are two members of this infinite family. Although the Bulk Lagrangian description of this family of theories is not currently known to us, the graviton scattering amplitudes in these theories are heavily constrained due to the existence of null states. Presumably they are exactly solvable in the same way as the minimal models of 2-D CFT.
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Acknowledgments
We would like to thank Andrew Strominger and Sabrina Pasterski for useful discussion. The work of SB is partially supported by the Swarnajayanti Fellowship (File No-SB/SJF/2021-22/14) of the Department of Science and Technology and SERB, India and by SERB grant MTR/2019/000937 (Soft-Theorems, S-matrix and Flat-Space Holography). The work of HK is partially supported by the KVPY fellowship of the Department of Science and Technology (DST), Government of India and the Summer Students’ Visiting Program at the Institute of Physics, Bhubaneswar, India. The work of PP is supported by an IOE endowed postdoctoral position at IISc, Bengaluru, India.
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Banerjee, S., Kulkarni, H. & Paul, P. An infinite family of w1+∞ invariant theories on the celestial sphere. J. High Energ. Phys. 2023, 63 (2023). https://doi.org/10.1007/JHEP05(2023)063
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DOI: https://doi.org/10.1007/JHEP05(2023)063