Generalized symmetry superalgebras

TL;DR

This paper extends the concept of symmetry superalgebras to include hidden symmetries generated by Killing spinors across all dimensions, revealing new algebraic structures and their geometric implications.

Contribution

It introduces a unified framework for generalized symmetry superalgebras incorporating hidden symmetries from Killing spinors in all dimensions.

Findings

Killing spinor bilinears generate special Killing-Yano forms

Constructs symmetry operators as generalized Lie derivatives

Provides explicit examples on weak G2 and nearly Kähler manifolds

Abstract

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano and special conformal Killing-Yano forms. After defining the Lie algebra structure of hidden symmetries generated by Killing spinors, we construct the symmetry operators as the generalizations of the Lie derivative on spinor fields. All these constructions together constitute the structure of generalized symmetry superalgebras. We exemplify the construction on weak $G_2$ and nearly K\"{a}hler manifolds.