Abstract
We find the conditions on compactifications of type IIA to four-dimensional Minkowski space to preserve \( \mathcal{N} \) = 2 supersymmetry in the language of Exceptional Generalized Geometry (EGG) and Generalized Complex Geometry (GCG). In EGG, off-shell \( \mathcal{N} \) =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 \( \mathcal{N} \) = 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.
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ArXiv ePrint: 1207.3004
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Graña, M., Orsi, F. \( \mathcal{N} \) = 2 vacua in generalized geometry. J. High Energ. Phys. 2012, 52 (2012). https://doi.org/10.1007/JHEP11(2012)052
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DOI: https://doi.org/10.1007/JHEP11(2012)052