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 N + 2 = 2 + N 1 and its supergroup extension. Finally, sl(2N) and the correspondence corresponding to 2N = N 2 is also analyzed.
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Pré-publication, Document de travail
2015
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  • HAL Id : hal-01242685, version 1
  • ARXIV : 1509.07516

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Thomas Creutzig, Yasuaki Hikida, Peter Rønne. Correspondences between WZNW models and CFTs with W -algebra symmetry. 2015. 〈hal-01242685〉

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