Instantons in two and four dimensions (Q1058220)

The purpose of this paper is to strengthen the analogy concerning the instantons in pure Yang-Mills theory in 4-dimensions and in the \(CP_ n\)-models in 2-dimensions. Essentially the author shows (at least for G a classical group and probably for all G) that Yang-Mills instantons in 4D can be naturally identified with (i.e. have the same parameter space as) the instantons in 2D for the theory in which the complex projective n- space \(CP_ n\) is replaced by the infinite-dimensional manifold \(\Omega\) G of loops on the structure group G.