Seeking SUSY fixed points in the 4-ε expansion

We use the 4 - epsilon expansion to search for fixed points corresponding to 2 + 1 dimensional 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 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 = N(N-1)/2 - 1 and O(N)/Z2 symmetry, that exists for arbitrary integer N >= 3.

Automated summary

The study focuses on searching for fixed points of 2+1 dimensional N=1 Wess-Zumino models of scalar superfields interacting through a cubic superpotential using the 4-epsilon expansion. Different classifications and analyses of fixed points in cases of N-Phi = 3, 4, and 5 are conducted, with a particular emphasis on irreducible fixed points where scalar superfields form a single irreducible representation of the symmetry group.