  We initiate the study of how the insertion of magnetically charged states in
4d self-dual gauge theories impacts the 2d chiral algebras supported on the
celestial sphere at asymptotic null infinity, from the point of view of the
4d/2d twistorial correspondence introduced by Costello and the second author.
By reducing the 6d twistorial theory to a 3d holomorphic-topological theory
with suitable boundary conditions, we can motivate certain non-perturbative
enhancements of the celestial chiral algebra corresponding to extensions by
modules arising from 3d boundary monopole operators. We also identify the
insertion of 4d (non-abelian) monopoles with families of spectral flow
automorphisms of the celestial chiral algebra.
