Multicollinear Singularities in Celestial CFT

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 ${\varphi }^3$ theory. In particular, we find that in ${\varphi }^3$ 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.

arXiv comment19 pages

References in corpus (9)

• A Conformal Basis for Flat Space Amplitudes
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Multi-Gluon Collinear Limits from MHV diagrams
• On Effective Field Theories with Celestial Duals
• Goldilocks Modes and the Three Scattering Bases
• Descendants in celestial CFT and emergent multi-collinear factorization
• Celestial Locality and the Jacobi Identity
• Celestial Conformal Colliders
• Detector Operators for Celestial Symmetries

Cited by in corpus (6)

• Celestial Gluon Amplitudes from the Outside In
• Currents in Celestial CFT
• Multiparticle Contributions to the Celestial OPE
• Non-abelian soft radiation data for a celestial theory
• Double-soft limit and celestial shadow OPE from charge bracket
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle