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On mirror symmetry with fluxes

We review a proposal for mirror symmetry on general six‐dimensional backgrounds involving manifolds admitting SU(3) structure and NS three‐form flux. The action of twisted covariant derivatives on invariant spinors leads to definition of complexified intrinsic torsion and most of the information about the geometry and the flux is encoded in terms of (real part of) a certain six‐by‐six matrix. Mirror symmetry exchanges the (1,1) and (2,0) components of this matrix.