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

TL;DR

This paper introduces a generalized Inonu-Wigner contraction to correctly derive the flat limit of the Wess-Zumino term for superstrings in AdS space, addressing issues with the standard contraction.

Contribution

It proposes a new generalized contraction method that yields a nondegenerate super-Poincare group, enabling proper flat limit analysis of the Wess-Zumino term.

Findings

Standard contraction yields zero in flat limit

Generalized contraction produces correct flat limit

Derived M-algebra from osp(1|32)

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).