I am studying D$p$-brane polarization (Myer's effect https://arxiv.org/abs/hep-th/9910053) and brane-flux annihilation (KPV mechanism, https://arxiv.org/abs/hep-th/0112197). There is little to no attention to fermionic background and worldvolume fields - the classical "you can add fermions here, but we will skip this discussion/we will not use it".
I always hear that the reasons are that 1) (semi?) classically you not expect fermions around, so it is safe to neglect them and 2) in line with the KPV, which is supposed to give rise to a maximally symmetric vacuum in four-dimensions, fermions should not be a cooking ingredient, since the vacuum expectations values for fermions in maximally symmetric spacetimes should be zero.
It sounds very vague to me, but I cannot really find better explanations in literature. Any explanation or reference, less vague than the aforementioned ones?