Celestial Locality and the Jacobi Identity

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We show the equivalence of several different tests of the Jacobi identity for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT.

• Along the way we clarify the role of the order of soft and collinear limits in obstructing Jacobi for soft insertions and we argue that, despite their current-algebra-like properties, soft insertions as formulated in this paper cannot be interpreted as local operators in celestial conformal field theory.