Killing Spinors and Related Symmetries in Six Dimensions

TL;DR

This paper uses an index spinorial formalism to solve and classify Killing spinor equations in six-dimensional spacetimes, revealing conditions on scalar curvature and Einstein properties, and explicitly deriving related tensors.

Contribution

It introduces a method to integrate and classify Killing spinors in six dimensions, and explicitly expresses associated KY and CCKY tensors from Killing spinors.

Findings

Killing spinor equations are integrated in six dimensions.

Two algebraic types of Killing spinors are classified based on curvature.

Explicit expressions for KY and CCKY tensors derived from Killing spinors.

Abstract

Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified in two algebraic types, in the first type the scalar curvature of the spacetime must be negative, while in the second type the spacetime must be an Einstein manifold. In addition, the equations that define Killing-Yano (KY) and closed conformal Killing-Yano (CCKY) tensors are expressed in the index notation and, as consequence, all non-vanishing KY and CCKY tensors that can be generated from a Killing spinor are made explicit.