Wess-Zumino term for the AdS superstring and generalized Inönü-Wigner contraction

Abstract

We examine a Wess-Zumino term, written in a form of bilinear in superinvariant currents, for a superstring in anti-de Sitter (AdS) space, and derive a procedure for obtaining the correct flat limit. The standard Inönü-Wigner contraction does not give the correct flat limit but, rather, gives zero. This erroneous result originates from the fact that the fermionic metric of the super-Poincaré group is degenerate. We propose a generalization of the InönüWigner contraction from which a "nondegenerate" super-Poincaré group is derived from the super-AdS group. For this reason, this contraction gives the correct flat limit of this Wess-Zumino term. We also discuss the M-algebra obtained using this generalized Inönü -Wigner contraction from osp(1|32).