Symmetry operators of Killing spinors and superalgebras in AdS_5

TL;DR

This paper constructs symmetry operators for Killing spinors using Killing-Yano forms in AdS_5, revealing an algebraic structure and exploring superalgebra extensions involving higher-degree forms.

Contribution

It introduces a novel algebraic framework for Killing spinor symmetry operators using Killing-Yano forms and investigates superalgebra extensions in AdS_5.

Findings

Symmetry operators close into an algebra in AdS_5.

A superalgebra extension exists, but no Lie superalgebra extension is possible.

The algebraic structure relates to extended Killing superalgebras.

Abstract

We construct the first-order symmetry operators of Killing spinor equation in terms of odd Killing-Yano forms. By modifying the Schouten-Nijenhuis bracket of Killing-Yano forms, we show that the symmetry operators of Killing spinors close into an algebra in AdS_5 spacetime. Since the symmetry operator algebra of Killing spinors corresponds to a Jacobi identity in extended Killing superalgebras, we investigate the possible extensions of Killing superalgebras to include higher-degree Killing-Yano forms. We found that there is a superalgebra extension but no Lie superalgebra extension of the Killing superalgebra constructed out of Killing spinors and odd Killing-Yano forms in AdS_5 background.