Supersymmetry with non-geometric fluxes, or a $\beta$-twist in Generalized Geometry and Dirac operator

Understand

We study ten-dimensional supersymmetric vacua with NSNS non-geometric fluxes, in the framework of $\beta$-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)xSU(3) structure in Generalized Complex Geometry.