Multicollinear Singularities in Celestial CFT

TL;DR

This paper investigates the holomorphic multicollinear limits of celestial amplitudes, revealing how branch cuts in certain theories affect the celestial operator product expansion and the validity of celestial Jacobi identities.

Contribution

It introduces the notion of holomorphic multicollinear limits, derives 3-collinear splitting functions for various theories, and shows how branch cuts impact celestial OPE associativity.

Findings

Branch cuts in $\,\phi^3$ theory obstruct the double residue condition.

Explicit 3-collinear splitting functions derived for Yang-Mills, gravity, and $\,\phi^3$ theories.

Multi-particle channels introduce new terms in celestial OPEs.

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 $\phi^3$ theory. In particular, we find that in $\phi^3$ 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.