Bootstrapping O(N) vector models with four supercharges in 3 ≤ d ≤ 4

We analyze the conformal bootstrap constraints in theories with four supercharges and a global O(N) x U(1) flavor symmetry in 3 <= d <= 4 dimensions. In particular, we consider the 4-point function of O(N)-fundamental chiral operators Z(i) that have no chiral primary in the O(N)-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of N + 1 chiral super-fields with superpotential W = X Sigma(N)(i=1) Z(i)(2), as well as general bounds on SCFTs where Sigma(N)(i=1) Z(i)(2) vanishes in the chiral ring.