Correspondences among CFTs with different W-algebra symmetry

Abstract

W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra $\mathfrak{g}$ and an $\mathfrak{sl}(2)$-embedding into $\mathfrak{g}$. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same $\mathfrak{g}$ but distinct $\mathfrak{sl}(2)$-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 $\mathfrak{g}=\mathfrak{sl}(3)$, 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 $\mathfrak{sl}(3)$, the Bershadsky-Polyakov algebra and the principal $W_3$-algebra. There are three non-regular W-algebras associated to $\mathfrak{g}=\mathfrak{sl}(4)$. We show that the methods developed for $\mathfrak{g}=\mathfrak{sl}(3)$ can be applied straightforwardly. We briefly comment on extensions of our techniques to general $\mathfrak{g}$.

arXiv comment52 pages

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Cited by in corpus (7)

• Duality of subregular W-algebras and principal W-superalgebras
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Higher rank FZZ-dualities
• Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
• FZZ-triality and large $\mathcal{N}=4$ super Liouville theory
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras
• Relaxed and logarithmic modules of $\widehat{{\mathfrak{sl}}_3}$