Spinor bilinears and Killing-Yano forms in generalized geometry

TL;DR

The paper extends Killing–Yano theory to generalized geometry by formulating KY-type equations for generalized $p$-forms using the $H$-twisted generalized connection $\mathbb{D}^H$ and by relating these forms to bilinears of generalized Killing and twistor spinors. It derives explicit generalized KY and closed conformal KY equations, clarifies how spinor bilinears correspond to odd KY and even CKY structures, and shows that sums over parities yield generalized conformal KY forms. The work also establishes a link to generalized Killing superalgebras, suggesting new hidden-symmetry frameworks in flux backgrounds. These results provide a mathematically intrinsic way to analyze symmetries in generalized geometries relevant to supergravity and string theory contexts.

Abstract

Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found. Killing equation in generalized geometry is written in terms of the generalized covariant derivative and Killing-Yano forms are described in the framework of generalized geometry. Construction of generalized Killing-Yano forms and generalized closed conformal Killing-Yano forms in terms of the spinor bilinears of generalized Killing spinors are determined.