N=2 vacua in Generalized Geometry

Abstract

We find the conditions on compactifications of type IIA to four-dimensional Minkowski space to preserve N=2 supersymmetry in the language of Exceptional Generalized Geometry (EGG) and Generalized Complex Geometry (GCG). In EGG, off-shell N =2 supersymmetry requires the existence of a pair of SU(2)_R singlet and triplet algebraic structures on the exceptional generalized tangent space that encode all the scalars (NS-NS and R-R) in vector and hypermultiplets respectively. We show that on shell N=2 requires, except for a single component, these structures to be closed under a derivative twisted by the NS-NS and R-R fluxes. We also derive the corresponding GCG-type equations for the two pairs of pure spinors that build up these structures.

34 pages

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• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• Generalised Structures for $\mathcal{N}=1$ AdS Backgrounds
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Generalized N=1 and N=2 structures in M-theory and type II orientifolds
• Supersymmetric AdS backgrounds and weak generalised holonomy
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Einstein Equations from Riemann-only Gravitational Actions