New constrained 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 composing a warped flux compactification AdS${}_3\times M_8$, whose metric and fluxes preserve one supersymmetry in AdS${}_3$. 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.

28 pages

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