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

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

arXiv comment29 pages, 5 tables, 1 figure

References in corpus (28)

• "Deconfined" quantum critical points
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Deconfined quantum critical points: symmetries and dualities
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Holography of the N=1 Higher-Spin Theory on AdS4
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• Decoding a Three-Dimensional Conformal Manifold
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Scalar CFTs and Their Large N Limits
• A challenge to the $a$-theorem in six dimensions
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• Bootstrapping the Minimal 3D SCFT
• On the finite subgroups of U(3) of order smaller than 512
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
• Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Bounds on multiscalar CFTs in the epsilon expansion
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions

Cited by in corpus (5)

• Line Defect RG Flows in the $\epsilon$ Expansion
• Bootstrapping Mixed MN Correlators in 3D
• Spontaneous breaking of finite group symmetries at all temperatures
• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Emergent Supersymmetry at Large $N$