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We analyze the conformal bootstrap constraints in theories with foursupercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq4$ 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 boundsthat nearly coincide with the theory of $N+1$ chiral super-fields withsuperpotential $W = X \sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTswhere $\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.

Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3 \leq d \leq4$