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W Algebras and Superalgebras from Constrained WZW Models: A Group Theoretical Classification

L. Frappat·E. Ragoucy·P. Sorba
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Abstract

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra) of a simple Lie algebra (resp. superalgebra) $\cg$. However, the determination of an $U(1)_Y$ factor, commuting with $Sl(2)$ (resp. $OSp(1|2)$), appears, when it exists, particularly useful to characterize the corresponding $W$ algebra. The (super) conformal spin contents of each $W$ (super)algebra is performed. The class of all the superconformal algebras (i.e. with conformal spins $s\leq2$) is easily obtained as a byproduct of our general results.

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L. Frappat, E. Ragoucy, P. Sorba. 1992-09-01. W Algebras and Superalgebras from Constrained WZW Models: A Group Theoretical Classification. https://doi.org/10.1007/bf02096881

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