Correspondences between WZNW models and CFTs with W -algebra symmetry

We study theories with w-algebra symmetries and their relation to wznw-type models on (super-)groups generalizing the h 3 + wznw to liouville correspondence. correlation functions of the wznw models are expressed in terms of correlators of cfts with w-algebra symmetry. the symmetries of the theories involved in these correspondences are related by the drinfeld-sokolov reduction of lie algebras to w-algebras. the w-algebras considered in this paper are the bershadsky-polyakov algebra for sl(3) and the quasi-superconformal algebra for generic sl(n|m). the quantum w-algebras obtained from affine sl(n) are constructed using embeddings of sl(2) into sl(n), and these can in turn be characterized by partitions of n. the above cases correspond to n + 2 = 2 + n 1 and its supergroup extension. finally, sl(2n) and the correspondence corresponding to 2 n = n 2 is also analyzed. these are all w-algebras that are generated by fields of at most dimension two.