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

TL;DR

The paper addresses obtaining a correct flat-space limit for the AdS superstring Wess-Zumino term by introducing a generalized Inönü-Wigner contraction that preserves next-to-leading terms in the Cartan forms. This method maps the super-AdS algebra to a nondegenerate super-Poincaré algebra, enabling a proper flat limit for the bilinear WZ term, and it clarifies the underlying M-algebra structure by deriving a reduced M-algebra from osp$(1|32)$. The authors illustrate the construction with a SO$(3)$ example and extend it to the AdS case, then connect it to Sezgin’s M-algebra via contractions, providing two realizations of the contracted algebras. The work offers a framework for obtaining nondegenerate, centrally extended supersymmetry algebras from AdS symmetries, with potential implications for p-brane dynamics and Chern-Simons supergravity in higher dimensions.

Abstract

We examine a Wess-Zumino term, written in bilinear of superinvariant currents, for a superstring in anti-de Sitter (AdS) space. The standard Inonu-Wigner contraction does not give the correct flat limit but gives zero. This originates from the fact that the fermionic metric of the super-Poincare group is degenerate. We propose a generalization of the Inonu-Wigner contraction which reduces the super-AdS group to the "nondegenerate" super-Poincare group, therefore it gives a correct flat limit of this Wess-Zumino term. We also discuss the M-algebra obtained by this generalized Inonu-Wigner contraction from osp(1|32).