Twistors, the ASD Yang-Mills equations and 4d Chern-Simons theory

A bstract We show that the approaches to integrable systems via 4d Chern-Simons theory and symmetry reductions of anti-self-dual Yang-Mills equations are closely related, at least classically. Following a suggestion Kevin Costello, we start from holomorphic on twistor space, defined with help meromorphic (3,0)-form ?. If ? is nowhere vanishing, it descends space-time classical motion equivalent equations. Examples include analogue Wess-Zumino-Witten model Lie algebra valued scalar cubic two derivative interaction. Under reduction, these yield actions for 2d systems. On other hand, performing reduction directly space reduces disorder defects studied by Costello & Yamazaki. Finally similar single translation leads 5d partially describing Bogomolny