On Sugawara construction on Celestial Sphere

TL;DR

This work analyzes the possibility of a Sugawara energy-momentum tensor in the celestial CFT by using conformally soft gluons to build a holomorphic Kac-Moody current algebra on the celestial sphere. Through Mellin-transform methods and double-soft limits of gluon amplitudes, it constructs T^S from currents and derives its OPE with soft gluons, fixing normalization and clarifying the soft-only Virasoro action. It then shows that T^S correctly generates conformal transformations for soft states but fails for hard states, motivating a refined tensor or a double-copy/shadow construction that can also address hard states and supertranslations. The paper further extends these ideas to general gauge groups and to Einstein–Yang–Mills theory, where a double-copy-inspired energy-momentum tensor and a supertranslation generator can be defined, offering a broader framework for CCFT symmetries and their holographic implications, while outlining open issues such as massive states and Wilson-line operators.

Abstract

Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills (EYM) theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.