Geometric algebra techniques in flux compactifications

Abstract

We study `constrained generalized Killing (s)pinors', which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently recover results pertaining to N=1 compactifications of M-theory on eight-manifolds.

70 pages

References in corpus (8)

• The Srni lectures on non-integrable geometries with torsion
• N=2 supersymmetric AdS_4 solutions of M-theory
• Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
• Symmetries of the Dirac operator with skew-symmetric torsion
• The geometric algebra of Fierz identities in arbitrary dimensions and signatures
• Hidden symmetry in the presence of fluxes
• Geometric algebra techniques in flux compactifications (II)
• Foliated eight-manifolds for M-theory compactification

Cited by in corpus (13)

• Geometric algebra techniques in flux compactifications (II)
• IIB supergravity on manifolds with SU(4) structure and generalized geometry
• Foliated eight-manifolds for M-theory compactification
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• New spinor classes on the Graf-Clifford algebra
• Spinors of real type as polyforms and the generalized Killing equation
• The duality covariant geometry and DSZ quantization of abelian gauge theory
• Choices of spinor inner products on M-theory backgrounds
• The Graf product: a Clifford structure framework on the exterior bundle
• Revisiting eight-manifold flux compactifications of M-theory using geometric algebra techniques
• A unified approach to Fierz identities
• New constrained generalized Killing spinor field classes in warped flux compactifications
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures