  The scattering of gluons and gravitons in trivial backgrounds is endowed with
many surprising infrared features which have interesting conformal
interpretations on the two-dimensional celestial sphere. However, the fate of
these structures in more general asymptotically flat backgrounds is far from
clear. In this paper, we consider holomorphic infrared structures in the
presence of non-perturbative, self-dual background gauge and gravitational
fields which are determined by freely specified radiative data. We make use of
explicit formulae for tree-level gluon and graviton scattering in these
self-dual radiative backgrounds, as well as chiral twistor sigma model
descriptions of the classical dynamics. Remarkably, we find that the leading
holomorphic part of tree-level collinear splitting functions -- or celestial
OPEs -- and infinite-dimensional chiral soft algebras are undeformed by the
background. We also compute all-order holomorphic celestial OPEs in the MHV
sectors of gauge theory and gravity.
