Conformal blocks from celestial gluon amplitudes

In celestial conformal field theory, gluons are represented by primary fields with dimensions = 1 + i lambda, lambda is an element of 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 + i lambda, 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.

Automated summary

In celestial conformal field theory, relaxation of constraints leads to four-point correlators containing conformal blocks of primary fields with specific dimensions and spins. These primary fields appear in compatible tensor product channels and contain continuous complex spins in incompatible channels.