Landscape of Simple Superconformal Field Theories in 4d

We explore the space of renormalization group flows that originate from $\mathcal{N}=1$ supersymmetric $SU(2)$ 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.