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

Abstract

Abstract Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional N $$ \mathcal{N} $$ = 1 Wess-Zumino models with cubic superpotetential W ∼ d ijk Φ i Φ j Φ k $$ \mathcal{W}\sim {d}_{ijk}{\Phi}^i{\Phi}^j{\Phi}^k $$ . 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 F 4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator d ijk Φ j Φ k is a (super)descendant of Φ i . We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field ∆Φ.

Keywords

• Conformal Field Theory
• Supersymmetric Gauge Theory