W-algebras and superalgebras from constrained WZW models: A group theoretical classification |
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| Authors: | L. Frappat E. Ragoucy P. Sorba |
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| Affiliation: | (1) Laboratoire de Physique Théorique ENSLAPP, Groupe d'Annecy, LAPP, Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex, France;(2) Groupe de Lyon, ENS Lyon, 46 allée d'Italie, F-69364 Lyon Cedex 07, France;(3) Present address: URA 14-36 du CNRS, associée à l'E.N.S. de Lyon, et au L.A.P.P. (IN2P3-CNRS), Lyon, France |
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| Abstract: | We present a classification ofW algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with anSl(2) subalgebra (resp.OSp(1/2) superalgebra) of a simple Lie algebra (resp. superalgebra)G. However, the determination of anU(1)Y factor, commuting withSl(2) (resp.OSp(1/2)), appears, when it exists, particularly useful to characterize the correspondingW algebra. The (super) conformal spin contents of eachW (super) algebra is performed. The class of all the superconformal algebras (i.e. with conformal spinss<=2) is easily obtained as a byproduct of our general results. |
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