Modified pure spinors and mirror symmetry

It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU(3) structure. We show that quantities involved in stability conditions for topological D-branes, and containing gauge fields in their expressions, are exchanged by mirror symmetry. This exchange can be considered as an open-string version of the mirror symmetry between pure spinors. It emerges from the fact that the modified pure spinors come out as moment maps for the symmetries of A and B models. The modification by the gauge field is argued to ensure the inclusion into the mirror exchange of the A-model non-Lagrangian branes endowed with a non-flat connection. Treating the connection as a distribution on an ambient six-manifold, assumed to be T3-fibered, the proposed mirror formula is established by fiberwise T-duality.