BRST analysis of super Kac-Moody and superconformal current algebras

The BRST charges are constructed for the supersymmetric extension of affine Kac-Moody algebras and for their semidirect sum with the superconformal algebra. In both cases, the BRST charge can be nilpotent only if the central charge of the super-Kac-Moody algebra representation vanishes. For general values of the central charge, it is shown by separating the positive and negative root contributions, that nilpotent operators can still be constructed. The associated cohomology is similar to the one introduced by Banks and Peskin for the Virasoro algebra. (orig.)