From Super-AdS_5xS^5 Algebra to Super-pp-wave Algebra

TL;DR

The paper demonstrates that the maximally supersymmetric IIB pp-wave algebra arises as an Inonu-Wigner contraction of the $AdS_5\times S^5$ superalgebra via the Penrose limit, with two contraction scales $R$ and $R'$ and a Penrose parameter $\Omega$ guiding the procedure. It shows Jacobi identities are preserved across the contraction, so supersymmetry remains intact, and imposes $R=R'$ to obtain the $(32)$-supercharge pp-wave algebra joseIIB, while the flat limit $R\to\infty$ yields flat supersymmetry. This work provides a coordinate-independent, algebraic bridge linking AdS$_5\times S^5$ and IIB plane-wave backgrounds, enabling straightforward derivations of brane actions and flux mappings in the pp-wave regime. The results illuminate how the AdS/CFT-related limit captures the plane-wave symmetry structure and offers a practical route to study dynamics in the pp-wave background.

Abstract

The isometry algebras of the maximally supersymmetric solutions of IIB supergravity are derived by the Inonu-Wigner contractions of the super-AdS_5xS^5 algebra. The super-AdS_5xS^5 algebra allows introducing two contraction parameters; the one for the Penrose limit to the maximally supersymmetric pp-wave algebra and the AdS_5xS^5 radius for the flat limit. The fact that the Jacobi identity of three supercharges holds irrespectively of these parameters reflects the fact that the number of supersymmetry is not affected under both contractions.