Abstract: I will briefly introduce the idea behind the conformal bootstrap, a program aiming - in it's most ambitious form - to classify conformal field theories (CFTs) in $d>2$. For the case of $d=4$, it recently became possible to consider CFTs with fermions, after the calculations of the relevant "Conformal Blocks" in arXiv:1601.05325. As an application I will consider the bootstrap equations of 2 scalars and 2 fermions. Solving these equations, in a particular limit, constrains the scaling dimensions of the large spin sector of the CFT.
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