Bootstrapping the $$ \mathcal{N} $$ = 1 Wess-Zumino models in three dimensions

Abstract

Abstract Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $$ \mathcal{N} $$ N = 1 Wess-Zumino models with cubic superpotetential $$ \mathcal{W}\sim {d}_{ijk}{\Phi}^i{\Phi}^j{\Phi}^k $$ W ∼ d ijk Φ i Φ j Φ k . The tensor dijk is taken to be the invariant tensor of either permutation group SN, special unitary group SU(N), or a series of groups called F4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator dijkΦjΦk is a (super)descendant of Φi. We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field ∆Φ.