Abstract
We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in [9] from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed w1+∞ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.
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Ren, L., Spradlin, M., Srikant, A.Y. et al. On effective field theories with celestial duals. J. High Energ. Phys. 2022, 251 (2022). https://doi.org/10.1007/JHEP08(2022)251
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DOI: https://doi.org/10.1007/JHEP08(2022)251