Geometric algebra techniques in flux compactifications (II)

Abstract

We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions for the metric and fluxes of the unit section of such cylinders and cones into differential and algebraic constraints on collections of differential forms defined on the cylinder or cone. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As a non-trivial application, we consider the most general N=2 compactification of eleven-dimensional supergravity on eight-manifolds.

56 pages, 2 figures, some commutative diagrams

References in corpus (6)

• 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
• Hidden symmetry in the presence of fluxes
• Geometric algebra techniques in flux compactifications

Cited by in corpus (19)

• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• The geometric algebra of Fierz identities in arbitrary dimensions and signatures
• IIB supergravity on manifolds with SU(4) structure and generalized geometry
• Foliated eight-manifolds for M-theory compactification
• Geometric algebra techniques in flux compactifications
• M-theory Compactifications to Three Dimensions with M2-brane Potentials
• $N=(2,0)$ 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
• A generalization of Calabi-Yau fourfolds arising from M-theory compactifications
• Choices of spinor inner products on M-theory backgrounds
• Foliated backgrounds for M-theory compactifications (II)
• Revisiting eight-manifold flux compactifications of M-theory using geometric algebra techniques
• Five-dimensional null & time-like supersymmetric geometries
• A unified approach to Fierz identities
• Singular foliations for M-theory compactification
• The landscape of G-structures in eight-manifold compactifications of M-theory
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures
• Geometric algebra and M-theory compactifications