Celestial Yang-Mills amplitudes and D = 4 conformal blocks

• DOI: 10.1007/jhep09(2022)182
• Publication Date: 2022-09-22T07:03:00Z
• Authors: Wei Fan; Angelos Fotopoulos; Stephan Stieberger; Tomasz R. Taylor; Bin Zhu
• Keywords: High Energy Physics - Theory; FOS: Physical sciences; QC770-798; Conformal and W Symmetry; 01 natural sciences; Scale and Conformal Symmetries; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Scattering Amplitudes; Duality in Gauge Field Theories

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 Kač-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.