Killing Spinor Equations from Nonlinear Realisations

TL;DR

This paper derives Killing spinor equations for eleven-dimensional supergravity and ten-dimensional N=1 supergravity from a nonlinear algebraic framework based on E11, providing a new algebraic perspective on supersymmetry conditions.

Contribution

It introduces a super extended algebra from nonlinear realisations of G11, reproducing Killing spinor equations covariantly, linking algebraic structures to supergravity supersymmetry conditions.

Findings

Derived Killing spinor equations from algebraic structures.

Connected E11-based algebra to supergravity supersymmetry.

Provided a unified algebraic approach to supersymmetry equations.

Abstract

Starting from a nonlinear realisation of eleven dimensional supergravity based on the group G11, whose generators appear as low level generators of E11, we present a super extended algebra, which leads to a covariant derivative of spinors identical to the Killing spinor equation of this theory. A similar construction leads to the Killing spinor equation of N=1 pure supergravity in ten dimensions.