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

Abstract

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional N = 1 Wess-Zumino models with cubic superpotetential $W\sim d_{ijk}{\Phi }_i{\Phi }_j{\Phi }_k$. The tensor $d_{ijk}$ is taken to be the invariant tensor of either permutation group $S_N$, 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 $d_{ijk}{\Phi }_i{\Phi }_j{\Phi }_k$ is a (super)descendant of ${\Phi }_i$ . We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field ${\Phi }_i$.

19 pages, 8 figures