Twistors, harmonics and holomorphic Chern-Simons

We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator ∂¯¯¯ is constructed from a complex-real (CR) structure of harmonic space. We also show that the local spacetime operators can be written as a Penrose transform on the coset SU(3)/(U(1) × U(1)). We observe a strong similarity to ambitwistor space constructions.ISSN:1126-6708ISSN:1029-847