On Sugawara construction on Celestial Sphere

TL;DR

This paper constructs and analyzes the Sugawara energy-momentum tensor in celestial conformal field theory, exploring its properties in Yang-Mills and Einstein-Yang-Mills theories and extending to supertranslations.

Contribution

It introduces a new Sugawara construction for the CCFT energy-momentum tensor and proposes an alternative tensor in EYM theory that correctly generates conformal transformations.

Findings

Sugawara tensor verifies Virasoro primaries for soft gluons.

Standard Sugawara tensor fails to generate correct transformations for hard states.

Alternative energy-momentum tensor in EYM theory correctly acts on both soft and hard states.

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.