New generalized Killing spinor field classes in warped flux compactifications

Abstract

The generalized Fierz identities are addressed in the Kähler–Atiyah bundle framework from the perspective of the equations governing constrained generalized Killing spinor fields. We explore the spin geometry in a Riemannian 8-manifold, $M_8$, composing a warped flux compactification AdS${}_3\times M_8$, whose metric and fluxes preserve one supersymmetry in AdS₃. Supersymmetry conditions can be efficiently translated into spinor bilinear covariants, whose algebraic and differential constraints yield identifying new spinor field classes. Intriguing implications and potential applications are discussed.