Uniqueness of M-theory PP-Wave Background with Extra Supersymmetries

TL;DR

This paper classifies eleven-dimensional pp-wave backgrounds with extra supersymmetries, showing they can be simplified to specific forms and analyzing their super-isometry algebras.

Contribution

It provides a classification of M-theory pp-wave backgrounds with additional supersymmetries and derives their super-isometry algebras.

Findings

Backgrounds with extra Killing spinors can be reduced to specific quadratic forms.

The form of the flux and metric is constrained by the presence of extra supersymmetries.

Super-isometry algebras of these backgrounds are explicitly derived.

Abstract

We examine Killing spinor equations of the general eleven-dimensional pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a three-form \xi(x^m,x^-) in the flux. Considering non-harmonic extra Killing spinors, we show that if the backgrounds admit at least one extra Killing spinor in addition to the standard 16 Killing spinors, they can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-) modulo coordinate transformations. We further examine the cases in which the extra Killing spinor is characterized by a set of Cartan matrices. The super-isometry algebras of the resulting backgrounds are also derived.