  It has been recently argued that inserting a probe anti-D3-brane in a flux
background breaks supersymmetry spontaneously instead of explicitly, as
previously thought. In this paper we argue that such spontaneous breaking of
supersymmetry persists even when the probe anti-D3-brane is kept in a curved
background with an internal space that doesn't have to be a Calabi-Yau
manifold. To show this we take a specific curved background generated by
fractional three-branes and fluxes on a non-Kahler resolved conifold where
supersymmetry breaking appears directly from certain world-volume fermions
becoming massive. In fact this turns out to be a generic property even if we
change the dimensionality of the anti-brane, or allow higher order fermionic
interactions on the anti-brane. We argue for the former by taking a probe
anti-D7-brane in a flux background and demonstrate the spontaneous breaking of
supersymmetry using world-volume fermions. We argue for the latter by
constructing an all order fermionic action for the anti-D3-brane from which the
spontaneous nature of supersymmetry breaking can be demonstrated by bringing it
to a kappa-symmetric form.
