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

TL;DR

This paper uses numerical bootstrap techniques to determine critical exponents and operator dimensions in three-dimensional N=1 Wess-Zumino models with specific superpotentials, revealing super-multiplet recombination effects.

Contribution

It introduces a numerical bootstrap approach to analyze 3D N=1 Wess-Zumino models with various symmetry groups, providing new insights into operator dimensions and supermultiplet structure.

Findings

Determined critical exponents for models with different symmetry groups.

Observed super-multiplet recombination at the fixed point.

Calculated the scaling dimension of the super-field i.

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 $\Phi_i$.