Correspondences between WZNW models and CFTs with W-algebra symmetry
Abstract
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(2 N) 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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- February 2016
- DOI:
- 10.1007/JHEP02(2016)048
- arXiv:
- arXiv:1509.07516
- Bibcode:
- 2016JHEP...02..048C
- Keywords:
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- Conformal and W Symmetry;
- Conformal Field Models in String Theory;
- High Energy Physics - Theory
- E-Print:
- 42 pages