Landscape of Simple Superconformal Field Theories in 4d

TL;DR

This paper maps out the landscape of simple 4d superconformal field theories emerging from RG flows of N=1 supersymmetric SU(2) gauge theories, revealing 34 fixed points with novel phenomena and 36 candidate theories with unusual properties.

Contribution

It systematically explores all relevant deformations of a basic supersymmetric gauge theory, discovering new fixed points and phenomena, including theories with unprecedented central charge values.

Findings

Identified 34 fixed points with emergent symmetry and operator decoupling.

Discovered theories with central charges smaller than any previously known superconformal theories.

Found 36 candidate theories with unphysical fermionic operators, including one with extremely low central charges.

Abstract

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.