Seeking SUSY fixed points in the \(4-\epsilon\) expansion. (English) Zbl 1521.81320

Summary: 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 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 \(N_\Phi = \frac{N(N-1)}{2} - 1\) and \(\mathrm{O}(N)\)/Z2 symmetry, that exists for arbitrary integer \(N \geq 3\).


81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T17 Renormalization group methods applied to problems in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81V05 Strong interaction, including quantum chromodynamics


Full Text: DOI arXiv


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