Celestial Locality and the Jacobi Identity

TL;DR

This paper establishes multiple equivalent criteria for the Jacobi identity in celestial currents at tree level, providing a practical condition on 4-point amplitudes in EFTs and clarifying the role of soft and collinear limits.

Contribution

It introduces a simple, practical condition for Jacobi identity verification in celestial current algebra and clarifies the limitations of soft insertions as local operators in celestial CFT.

Findings

Multiple tests of Jacobi identity are shown to be equivalent.

A practical condition on 4-point amplitudes is derived.

Soft insertions cannot be interpreted as local operators in celestial CFT.

Abstract

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.