A twistor space action for Yang-Mills theory

We consider the twistor space P-6 congruent to R-4 x CP1 of R-4 with a nonintegrable almost complex structure J such that the canonical bundle of the almost complex manifold (P-6, J) is trivial. It is shown that J-holomorphic Chern-Simons theory on a real (6 vertical bar 2)-dimensional graded extension P-6 vertical bar 2 of the twistor space P-6 is equivalent to self-dual Yang-Mills theory on Euclidean space R-4 with Lorentz invariant action. It is also shown that adding a local term to a Chern-Simons-type action on P-6 vertical bar 2, one can extend it to a twistor action describing full Yang-Mills theory.

Automated summary

By combining Chern-Simons theory with Twistor space, a complete Yang-Mills theory description can be established on P-6 | 2.