Twistor spinors and extended conformal superalgebras

TL;DR

This paper explores how symmetry operators of twistor spinors relate to conformal Killing-Yano forms in conformally-flat backgrounds, extending conformal superalgebras with new algebraic structures relevant to supersymmetry.

Contribution

It introduces a method to construct symmetry operators from conformal Killing-Yano forms and extends conformal superalgebras using graded Lie algebra structures.

Findings

Symmetry operators of twistor spinors can be built from conformal Killing-Yano forms.

Conditions for mutually commuting symmetry operators are established.

Extended superalgebras incorporate conformal Killing-Yano forms and twistor spinors.

Abstract

We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of conformal Killing vectors and twistor spinors and play important roles in supersymmetric field theories in conformal backgrounds are extended to more general superalgebras by using the graded Lie algebra structure of conformal Killing-Yano forms and the symmetry operators of twistor spinors. The even part of the extended conformal superalgebra corresponds to conformal Killing-Yano forms and the odd part consists of twistor spinors.