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

We analyze the conformal bootstrap constraints in theories with four supercharges and a global \(O(N) \times U(1)\) flavor symmetry in \(3 \leq d \leq 4\) 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 \(W = X \sum_{i=1}^N Z_i^2\), as well as general bounds on SCFTs where \(\sum_{i=1}^N Z_i^2\) vanishes in the chiral ring.