W-strings from N = 2 Hamiltonian Reduction and Classification of N = 2 Super W-algebras

We present an algebraic approach to string theory, using a Hamiltonian reduction of N = 2 WZW models. An embedding of sl(1|2) in a Lie superalgebra determines a niltopent subalgebra. Chirally gauging this subalgebra in the corresponding WZW action leads to an extension of the N = 2 superconformal algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this provides an exhaustive classification and characterization of all extended N = 2 superconformal algebras. Then, twisting these algebras, we obtain the BRST structure of a string theory. We characterize and classify all the string theories which can be obtained in this way.