Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3\le d\le 4$

Abstract

We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N)\times U(1)$ flavor symmetry in $3\le d\le 4$ 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.

25 pages, 8 figures