No isomorphism between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras

Abstract

Since 1999 it became obvious that the would be `isomorphism' between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in the literature and, as a result, some confusion still remains. In this article we finally settle down, clearly and unambiguously, the true facts: there is no isomorphism between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras.