Correspondences among CFTs with different W-algebra symmetry
Thomas Creutzig, Naoki Genra, Yasuaki Hikida, Tianshu Liu
Abstract
W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra g and an sl(2)-embedding into g. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same g but distinct sl(2)-embeddings. For this purpose, we first explore different free field realizations of W-algebras and then generalize previous works on the path integral derivation of correspondences of correlation functions. For g=sl(3), there is only one non-standard (non-regular) W-algebra known as the Bershadsky-Polyakov algebra. We examine its free field realizations and derive correlator correspondences involving the WZNW theory of sl(3), the Bershadsky-Polyakov algebra and the principal W3-algebra. There are three non-regular W-algebras associated to g=sl(4). We show that the methods developed for g=sl(3) can be applied straightforwardly. We briefly comment on extensions of our techniques to general g.