  We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its
lift to holomorphic BF theory on twistor space. Following the work of Costello
and Paquette, we couple SDYM to a quartic axion field, which guarantees
associativity of the (extended) celestial chiral algebra at the quantum level.
We demonstrate how to reproduce their one-loop quantum deformation to the
chiral algebra using Koszul duality.
