Fermions on the Anti-Brane: Higher Order Interactions and Spontaneously Broken Supersymmetry

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.