Supersymmetry and Kac-Moody algebras

The invariance algebra of the Majorana action contains a Kac-Moody algebra which, ''on shell'', reduces to an Abelian algebra. In the absence of auxiliary fields in the Wess-Zumino model, supersymmetry transformations generate an infinite-dimensional Lie algebra, which is shown to be a Grassmannian extension of this Kac-Moody algebra. The corresponding Noether charges are discussed. (orig.)