Landscape of Simple Superconformal Field Theories in 4D

We explore the space of renormalization group flows that originate from supersymmetric $\mathcal{N}=1$ $SU(2)$ gauge theory with one adjoint and a pair of fundamental chiral multiplets. By considering all possible relevant deformations—including coupling to gauge-singlet chiral multiplets—we find 34 fixed points in this simple setup. We observe that theories in this class exhibit many novel phenomena: emergent symmetry, decoupling of operators, and narrow distribution of central charges $a/c$. This set of theories includes two of the $\mathcal{N}=2$ minimal Argyres-Douglas theories and their mass deformed versions. In addition, we find 36 candidate fixed point theories possessing unphysical fermionic operators—including one with central charges $(a,c)\simeq (0.20,0.22)$ that are smaller than any known superconformal theory—that need further investigation.

Figure 1

The central charges of the 34 “good” theories. The ratios $a/c$ all lie within the range (0.8246,0.9895). The mean value of $a/c$ is 0.8732, with standard deviation 0.0403.

Figure 2

A subset of the fixed points that can be obtained from $SU(2)N_f=1$ adjoint SQCD with singlets. The arrows are labeled with the superpotential deformations. Note that the graph is not arranged vertically by decreasing the $a$ central charge because the deformations we consider involve coupling in the singlet fields.