Fermions on the antibrane: Higher order interactions and spontaneously broken supersymmetry

It has been recently argued that inserting a probe $\overline{\mathrm{D}3}$-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 $\overline{\mathrm{D}3}$-brane is kept in a curved background with an internal space that does not have to be a Calabi-Yau manifold. To show this we take a specific curved background generated by fractional 3-branes and fluxes on a non-Kähler resolved conifold where supersymmetry breaking appears directly from certain worldvolume fermions becoming massive. In fact this turns out to be a generic property even if we change the dimensionality of the antibrane, or allow higher-order fermionic interactions on the antibrane. We argue for the former by taking a probe $\overline{\mathrm{D}7}$-brane in a flux background and demonstrate the spontaneous breaking of supersymmetry using worldvolume fermions. We argue for the latter by constructing an all-order fermionic action for the $\overline{\mathrm{D}3}$-brane from which the spontaneous nature of supersymmetry breaking can be demonstrated by bringing it to a $\kappa$-symmetric form.

Figure 1

The type IIB moduli space with the self-dual point denoted by $A$. The point $B$ is for all $R_i=1$ and the point $C$ is for $g_s=1$. Our duality mappings are defined for the point $A$. Going away from the point $A$ in any direction in the moduli space will imply switching on nontrivial values for the axio-dilaton.