Celestial operator products from the worldsheet

TL;DR

This work demonstrates that the tree-level celestial OPEs of gluons and gravitons in CCFT can be dynamically generated from the worldsheet OPEs of vertex operators in four-dimensional ambitwistor strings. By analyzing conformal-primary vertex operators and their collisions, the authors reproduce the known CCFT OPE data and, remarkably, an infinite tower of $SL(2,\mathbb{R})$ descendants without truncation, across all helicities and particle configurations. They also construct operator realizations of the conformally soft symmetry algebras on ambitwistor space, obtaining explicit currents that generate soft gluon $\mathfrak{g}$ Kac-Moody and soft graviton $w_{1+\infty}$ algebras, along with their actions on hard states. In addition, the momentum-eigenstate OPEs reproduce collinear splitting functions, providing a cross-check via the momentum-space limit and establishing a coherent bridge between worldsheet dynamics, celestial holography, and standard amplitudes. Overall, the paper offers a concrete, dynamical realization of CCFT data within ambitwistor-string theory and lays groundwork for deeper connections between celestial holography and 2d CFTs on the celestial sphere.

Abstract

We compute the operator product expansions of gluons and gravitons in celestial CFT from the worldsheet OPE of vertex operators of four-dimensional ambitwistor string theories. Remarkably, the worldsheet OPE localizes on the short-distance singularity between vertex operator insertions which in turn coincides with the OPE limit of operator insertions on the celestial sphere. The worldsheet CFT dynamically produces known celestial OPE coefficients -- as well as infinite towers of SL$(2,\mathbb{R})$ descendant contributions to the celestial OPE -- without any truncations or approximations. We obtain these results for all helicities and incoming/outgoing configurations. Furthermore, the worldsheet OPE encodes the infinite-dimensional symmetry algebras associated with the conformally soft sectors of gauge theory and gravity. We provide explicit operator realizations of the currents generating these symmetries on ambitwistor space in terms of vertex operators for soft gluons and gravitons, also computing their actions on hard particles of all helicities. Lastly, we show that the worldsheet OPE for momentum eigenstates produces the collinear splitting functions of gluons and gravitons.