We consider the twistor space P6≅R4×CP1 of R4 with a nonintegrable almost complex structure J such that the canonical bundle of the almost complex manifold (P6,J) is trivial. It is shown that J-holomorphic Chern-Simons theory on a real (6|2)-dimensional graded extension P6|2 of the twistor space P6 is equivalent to self-dual Yang-Mills theory on Euclidean space R4 with Lorentz invariant action. It is also shown that adding a local term to a Chern-Simons-type action on P6|2, one can extend it to a twistor action describing full Yang-Mills theory.
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