Wess-Zumino term for AdS superstring

TL;DR

The paper introduces a pseudo-superinvariant bilinear Wess-Zumino term $\tilde{B}=B_{[2]}-d\bar{\theta}\,\tau_1\,d\theta$ for the AdS superstring, and proves it yields the correct three-form field strength $H_{[3]}$, preserves $\kappa$-invariance, and has the proper flat-space limit. It provides a concrete construction of global Noether charges for the super-AdS$_5\times$S$^5$ background and shows a topological string charge $Z$ appears in the supersymmetry algebra, vanishing for zero-modes but nonzero for excited states. The work emphasizes that a generalized IW contraction, preserving both $L_{1/2}$ and $L_{3/2}$, is necessary to obtain a nondegenerate flat limit of the bilinear WZ term, reflecting the nondegeneracy of the AdS superalgebra. These results clarify the existence and structure of bilinear WZ terms in AdS spaces and their implications for brane actions and flat-space limits.

Abstract

We examine a bilinear form Wess-Zumino term for a superstring in anti-de Sitter (AdS) spaces. This is composed of two parts; a bilinear term in superinvariant currents and a total derivative bilinear term which is required for the pseudo-superinvariance of the Wess-Zumino term. The covariant supercharge commutator containing a string charge is also obtained.