Physics – High Energy Physics – High Energy Physics - Theory

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1992-07-29

Commun.Math.Phys. 157 (1993) 499-548

Physics

High Energy Physics

High Energy Physics - Theory

66 pages (Latex), ENSLAPPP-A-391/92 Replaces previous unLatexable version, corrupted by mailer

Scientific paper

10.1007/BF02096881

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.

**Frappat Luc**

Physics – Biological Physics

Scientist

**Ragoucy Eric**

Physics – Condensed Matter – Statistical Mechanics

Scientist

**Sorba Paul**

Physics – Biological Physics

Scientist

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