Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks

TL;DR

This paper explores the structure of celestial four-gluon amplitudes, revealing their factorization into current and scalar parts, with the scalar component linked to conformal blocks and Coulomb gas models, advancing understanding in celestial holography.

Contribution

It demonstrates the factorization of celestial four-gluon amplitudes into current and scalar components, connecting them to Wess-Zumino-Witten correlators and conformal blocks.

Findings

Amplitude factorizes into current and scalar parts.

Scalar part expressed via complex integrals similar to Coulomb gas models.

Scalar component derived from dimensional reduction of D=4 conformal blocks.

Abstract

We discuss the properties of recently constructed "single-valued" celestial four-gluon amplitudes. We show that the amplitude factorizes into the "current" part and the "scalar" part. The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Ka\v{c}-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. The scalar part can be also obtained by a dimensional reduction of a single D=4 conformal block and the shadow block from Minkowski space to the celestial sphere.