Descendants in celestial CFT and emergent multi-collinear factorization

TL;DR

The paper develops a holographic approach to flat-space scattering via celestial CFT by deriving multi-collinear factorization limits from the CCFT operator product expansions. By leveraging asymptotic symmetries, it fixes conformal descendants and, for gluons, computes all-order OPE coefficients, then reproduces leading multi-gluon collinear limits through recursive CCFT methods and Mellin-transform consistency with momentum-space splitting functions. It extends these checks to gravitons in the leading sequential double-collinear regime, confirming consistency with the leading OPE of celestial gravitons. The results illustrate how locality and unitarity could emerge dynamically from CCFT data and offer a program to reconstruct bulk scattering from CCFT via the OPE bootstrap, with implications for subleading soft symmetries and potential color-kinematics dualities.

Abstract

Multi-collinear factorization limits provide a window to study how locality and unitarity of scattering amplitudes can emerge dynamically from celestial CFT, the conjectured holographic dual to gauge and gravitational theories in flat space. To this end, we first use asymptotic symmetries to commence a systematic study of conformal and Kac-Moody descendants in the OPE of celestial gluons. Recursive application of these OPEs then equips us with a novel holographic method of computing the multi-collinear limits of gluon amplitudes. We perform this computation for some of the simplest helicity assignments of the collinear particles. The prediction from the OPE matches with Mellin transforms of the expressions in the literature to all orders in conformal descendants. In a similar vein, we conclude by studying multi-collinear limits of graviton amplitudes in the leading approximation of sequential double-collinear limits, again finding a consistency check against the leading order OPE of celestial gravitons.