conformal blocks from celestial gluon amplitudes

• DOI: 10.48550/arxiv.2103.04420
• Publication Date: 2021-05-01
• Authors: Angelos Fotopoulos; Angelos Fotopoulos; Bin Zhu; Wei Fan; Tomasz R. Taylor; Stephan Stieberger
• Keywords: High Energy Physics - Theory; Conformal Field Theory; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; FOS: Physical sciences; QC770-798; Scattering Amplitudes; 16. Peace & justice; 01 natural sciences

Abstract In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ, λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ, where M ≥ 0 is an integer, with integer spin J = −M, −M + 2, …, M − 2, M. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.