Geometric Construction of Killing Spinors and Supersymmetry Algebras in Homogeneous Spacetimes

TL;DR

This paper presents a geometric and group-theoretical approach to construct Killing spinors and supersymmetry algebras in symmetric supergravity spacetimes, simplifying calculations for solutions like AdS, AdS×S, and Hpp-waves.

Contribution

It introduces a new geometric method for constructing Killing spinors and supersymmetry algebras in symmetric supergravity backgrounds, streamlining previous complex calculations.

Findings

Simplified construction of Killing spinors in symmetric spacetimes

Efficient calculation of supersymmetry algebras

Applicable to AdS, AdS×S, and Hpp-wave solutions

Abstract

We show how the Killing spinors of some maximally supersymmetric supergravity solutions whose metrics describe symmetric spacetimes (including $AdS,AdS\times S$ and H$pp$-waves) can be easily constructed using purely geometrical and group-theoretical methods. The calculation of the supersymmetry algebras is extremely simple in this formalism.