Abstract
The purpose of this paper is to study the holomorphic multicollinear limit of (celestial) amplitudes and use it to further investigate the double residue condition for (hard celestial) amplitudes and the celestial operator product expansion. We first set up the notion of holomorphic multicollinear limits of amplitudes and derive the 3-collinear splitting functions for Yang-Mills theory, Einstein gravity, and massless ϕ3 theory. In particular, we find that in ϕ3 theory the celestial 3-OPE contains a term with a branch cut. This explicit example confirms that branch cuts can obstruct the double residue condition for hard celestial amplitudes, which is the underlying cause of the celestial Jacobi identities not holding for certain theories. This addresses an ongoing debate in the literature about associativity of the celestial OPEs and concretely demonstrates a new (multi-particle) term in the celestial OPE coming from the multi-particle channel in the amplitudes.
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Acknowledgments
We would like to thank Justin Kulp, Andrzej Pokraka, and Akshay Yelleshpur Srikant for useful conversations, and Freddy Cachazo for comments on the draft. The research of AB, YH, and SP is supported by the Celestial Holography Initiative at the Perimeter Institute for Theoretical Physics and the Simons Collaboration on Celestial Holography. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities. AB was also supported by the US Department of Energy under contract DE-SC0010010 Task F and by Simons Investigator Award #376208.
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ArXiv ePrint: 2309.16602
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Ball, A., Hu, Y. & Pasterski, S. Multicollinear singularities in celestial CFT. J. High Energ. Phys. 2024, 219 (2024). https://doi.org/10.1007/JHEP02(2024)219
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DOI: https://doi.org/10.1007/JHEP02(2024)219