Nonlinear Lie conformal algebras and one-loop corrections of self-dual Yang–Mills amplitudes

Abstract This work is motivated by recent developments in celestial holography. In [15], the authors interpreted QCD collinear singularities in terms of operator product expansions in a two-dimensional CFT. We reformulate the algebraic structures arising in their work using the formalism of nonlinear Lie conformal algebras developed in [31].