Abstract
We study ten-dimensional supersymmetric vacua with NSNS non-geometric fluxes, in the framework of β-supergravity. We first provide expressions for the fermionic supersymmetry variations. Specifying a compactification ansatz to four dimensions, we deduce internal Killing spinor equations. These supersymmetry conditions are then reformulated in terms of pure spinors, similarly to standard supergravity vacua admitting an SU(3)×SU(3) structure in Generalized Complex Geometry. The standard d–H∧ acting on the pure spinors is traded for a generalized Dirac operator \( \mathcal{D} \), depending here on the non-geometric fluxes. Rewriting it with an exponential of the bivector β leads us to discuss the geometrical characterisation of the vacua in terms of a β-twist, in analogy to the standard twist by the b-field. Thanks to \( \mathcal{D} \), we also propose a general expression for the superpotential to be obtained from standard supergravities or β-supergravity, and verify its agreement with formulas of the literature. We finally comment on the Ramond-Ramond sector, and discuss a possible relation to intermediate or dynamical SU(2) structure solutions.
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Andriot, D., Betz, A. Supersymmetry with non-geometric fluxes, or a β-twist in Generalized Geometry and Dirac operator. J. High Energ. Phys. 2015, 6 (2015). https://doi.org/10.1007/JHEP04(2015)006
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DOI: https://doi.org/10.1007/JHEP04(2015)006