Correspondences between WZNW models and CFTs with W-algebra symmetry

Abstract

We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. 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 \underline{N+2} = \underline{2} + N \underline{1} and its supergroup extension. Finally, sl(2N) and the correspondence corresponding to \underline{2N} = N \underline{2} is also analyzed.

42 pages

References in corpus (12)

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Cited by in corpus (9)

• A slow review of the AGT correspondence
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Rectangular W-(super)algebras and their representations
• Correspondences among CFTs with different W-algebra symmetry
• Bispectral duality and separation of variables from surface defect transition
• Higher rank FZZ-dualities
• Conformal field theories from deformations of theories with $W_n$ symmetry
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras