W-ALGEBRAS AND SUPERALGEBRAS FROM CONSTRAINED WZW MODELS - A GROUP THEORETICAL CLASSIFICATION

We present a classification of W algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an Sl(2) subalgebra (resp. OSp(1\2) superalgebra) of a simple Lie algebra (resp. superalgebra) G. However, the determination of an U(1)Y factor, commuting with Sl(2) (resp. OSp(1\2)), appears, when it exists, particularly useful to characterize the corresponding W algebra. The (super) conformal spin contents of each W (super) algebra is performed. The class of all the superconformal algebras (i.e. with conformal spins s less-than-or-equal-to 2) is easily obtained as a byproduct of our general results.