Searching for integrability (Q1184392)

The self-dual Yang-Mills equations in four dimensions are integrable via the twistor transform for any gauge group. Integrability of the proper Yang-Mills equations in four dimensions with a finite dimensional gauge group cannot reasonably be hoped for. The author supports the conjecture that the limit \(\lim_{N\to \infty}\text{SU}(N)\) would lead to integrability in a certain, not strongly defined sense. In particular, as it has been shown a long time ago by t'Hooft, QCD theory becomes for \(\lim_{N\to\infty}\text{SU}(N)\) tractable. Manin, generalizing the Atiyah-Drinfeld-Hitchin-Manin construction, obtained for \(N\geq 66\) nonvacuous results. A concrete approach to \(\lim_{N\to \infty}\text{SU}(N)\) has not yet been proposed by the author.