Extended superalgebras from twistor and Killing spinors

TL;DR

This paper explores the mathematical structures of spinors, particularly twistor and Killing spinors, and constructs extended superalgebras using KY and CKY forms in specific geometric settings.

Contribution

It introduces a novel framework for building extended Killing and conformal superalgebras from KY and CKY forms in constant curvature and Einstein manifolds.

Findings

Constructed symmetry operators for Dirac equations.

Established graded Lie algebra structures for KY and CKY forms.

Developed extended superalgebras in specific geometric contexts.

Abstract

The basic first-order differential operators of spin geometry that are Dirac operator and twistor operator are considered. Special types of spinors defined from these operators such as twistor spinors and Killing spinors are discussed. Symmetry operators of massless and massive Dirac equations are introduced and relevant symmetry operators of twistor spinors and Killing spinors are constructed from Killing-Yano (KY) and conformal Killing-Yano (CKY) forms in constant curvature and Einstein manifolds. The squaring map of spinors gives KY and CKY forms for Killing and twistor spinors respectively. They constitute a graded Lie algebra structure in some special cases. By using the graded Lie algebra structure of KY and CKY forms, extended Killing and conformal superalgebras are constructed in constant curvature and Einstein manifolds.