  Recent works have explored how scattering amplitudes in quantum self-dual
Yang-Mills theory and self-dual gravity can be interpreted as resulting from an
anomaly, as first proposed by W. Bardeen. We study this problem in the
light-cone-gauge formulation of the theories. Firstly, we describe how the
infinite tower of symmetries associated to classical integrability can be
quantum corrected, exhibiting the one-loop anomaly. Secondly, we present
quantum-corrected light-cone Lagrangians worthy of the simplicity of the
amplitudes, building on recent works describing the anomaly in twistor space.
Finally, we discover an unexpected BCJ-like double copy for the
(loop-integrated) amplitudes, distinct from the well-known BCJ double copy for
the loop integrands.
