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We compute the four-dimensional gaugino mass for a Dp-brane extended inspacetime and wrapping a cycle on the internal geometry in a warpedcompactification with fluxes. Motivated by the backreaction of gaugino bilinearVEVs, we use Generalized Complex Geometry to characterize the internal geometryas well as the cycle wrapped by the brane. We find that the RR fluxes and thenon-closure of the generalized complex structures combine in the gaugino massterms in the same form as they do in the bulk superpotential, while for theNSNS fluxes there is a crucial minus sign in the component normal to the brane.Our expression extends the known result for D3 and D7-branes in Calabi-Yaumanifolds, where the gaugino masses are induced respectively by the imaginaryanti-self dual and imaginary self-dual components of the complex 3-form flux$G_3$.

Gaugino mass term for D-branes and Generalized Complex Geometry