Seeking SUSY fixed points in the $4-\epsilon$ expansion

TL;DR

This paper uses the 4−ε expansion to identify and classify supersymmetric fixed points in 2+1 dimensions for models with various numbers of superfields, revealing new fixed points with specific symmetry properties.

Contribution

It systematically classifies SUSY fixed points in Wess-Zumino models using the 4−ε expansion, including new families of fixed points with O(N)/Z2 symmetry for arbitrary N.

Findings

Identified all SUSY fixed points for N_Φ=3.

Found a unique fully interacting fixed point for N_Φ=4 with S5 symmetry.

Discovered a new family of fixed points with O(N)/Z2 symmetry for N≥3.

Abstract

We use the $4-\epsilon$ expansion to search for fixed points corresponding to $2+1$ dimensional $\mathcal{N}$=1 Wess-Zumino models of $N_{\Phi}$ scalar superfields interacting through a cubic superpotential. In the $N_{\Phi}=3$ case, we classify all SUSY fixed points that are perturbatively unitary. In the $N_{\Phi}=4$ and $N_{\Phi}=5$ cases, we focus on fixed points where the scalar superfields form a single irreducible representation of the symmetry group (irreducible fixed points). For $N_{\Phi}=4$ we show that the S5 invariant super Potts model is the only irreducible fixed point where the four scalar superfields are fully interacting. For $N_{\Phi}=5$, we go through all Lie subgroups of O(5) and then use the GAP system for computational discrete algebra to study finite subgroups of O(5) up to order 800. This analysis gives us three fully interacting irreducible fixed points. Of particular interest is a subgroup of O(5) that exhibits O(3)/Z2 symmetry. It turns out this fixed point can be generalized to a new family of models, with $N_{\Phi}=\frac{\rm N(N-1)}{2}-1$ and O(N)/Z2 symmetry, that exists for arbitrary integer N$\geq3$.