The isomorphism between two-dimensional conformal field theories with the affine-$sl(2)$ and the $N=2$ superconformal symmetry algebras

We discuss the one-to-one correspondence between two-dimensional conformal field theories with the affine-$sl(2)$ and the $N=2$ superconformal symmetry algebras. We obtain the formulas relating zero-norm states in the two theories and the formulas expressing the partition function of the affine-$sl(2)$ theory through the partition function of the theory with the $N=2$ superconformal symmetry algebra, and vice versa.