Super-PP-wave Algebra from Super-AdS x S Algebras in Eleven-dimensions

TL;DR

This paper explores how maximally supersymmetric spacetime algebras in eleven dimensions are interconnected through Inonu-Wigner contractions, revealing how supersymmetries are preserved during these algebraic limits.

Contribution

It demonstrates the derivation of super-pp-wave algebra from super-AdS x S algebras via two contraction parameters, maintaining supersymmetry through Jacobi identity preservation.

Findings

Super-AdS x S algebras can be contracted to super-pp-wave algebra.

Supersymmetry is preserved during contractions due to Jacobi identity.

Two contraction parameters correspond to flat and Penrose limits.

Abstract

Maximally supersymmetric spacetime algebras in eleven-dimensions, which are the isometry superalgebras of Minkowski space, AdS_7 x S^4, AdS_4 x S^7 and pp-wave background, are related by Inonu-Wigner contractions. The super-AdS_{4(7)} x S^{7(4)} algebras allow to introduce two contraction parameters, the one for the flat limit to the super-Poincare algebra and the other for a Penrose limit to the super-pp-wave algebra. Under these contractions supersymmetries are maintained because the Jacobi identity of three supercharges holds for any values of contraction parameters.