hoping to resolve some confusion I have about this paper (https://arxiv.org/abs/hep-th/9904017) regarding the holographic dual of a flow from ${\cal N}=4$ SYM to an ${\cal N}=1$ SUSY theory. Broadly speaking, this paper treats a model in which a mass term for one of the chiral superfields is introduced to the ${\cal N}=4$ theory. This induces a renormalization group flow to another ${\cal N}=1$ SCFT in the IR.
This deformation manifestly preserves N=1 SUSY, so the gravitational dual background should also preserve N=1 SUSY along the flow from the UV to the IR. My issue is essentially that the authors claim that along the flow, the solution preserves a single Majorana supersymmmetry. (See page 19, shortly after eq'n 5.2 for this statement)
My issue is with the term Majorana here. Normally in a 4D N=1 theory we have 4 independent supercharges organized into two Weyl spinors $Q^\alpha$ and $\bar{Q}_\dot{\alpha}$. I'm not sure precisely how to think about what it means for a symmetry generator to satisfy a Majorana condition, but it seems to me it should imply that these two spinors are no longer independent. That should leave us with only 2 independent SUSY generators. But that doesn't really make sense to me, I've never seen an N=1 SUSY theory like that and I don't see how the QFT on the field theory side should have any less than 4 supercharges.
I feel like I'm misunderstanding something really simple here but I'm not quite seeing what it is. Any help would be appreciated.
