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Landscape of Simple Superconformal Field Theories in 4d

Kazunobu Maruyoshi, Emily Nardoni, Jaewon Song

TL;DR

This work maps a landscape of simple four-dimensional ${\mathcal{N}}=1$ SCFTs generated from ${SU(2)}$ gauge theory with one adjoint and two fundamentals by exhaustively exploring relevant deformations, including gauge-singlet couplings. Using ${a}$-maximization and the superconformal index as primary viability tests, the authors identify ${34}$ good fixed points—among them two enhanced ${\mathcal{N}}=2$ Argyres–Douglas theories ${H_0}$ and ${H_1}$ and a minimal ${\mathcal{N}}=1$ theory ${H_0^*}$—as well as ${36}$ questionable fixed points with potential accidental symmetries and unphysical operators, notably a candidate minimal theory ${\mathcal{T}}_M$ with very small ${a}$ and ${c}$. The good theories exhibit emergent symmetry and operator decoupling, and their ${a}$ and ${c}$ values lie in a narrow band with ${a}/{c}\approx 0.87$, while the bad set hints at further structure (e.g., decoupled fermions) needed to resolve unitarity concerns. Overall, the paper provides a practical framework for enumerating and testing simple ${\mathcal{N}}=1$ SCFTs via Lagrangian RG flows, highlighting near-minimal theories and raising questions about IR accidental symmetries and the true minimal fixed point in this landscape.

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.

Landscape of Simple Superconformal Field Theories in 4d

TL;DR

This work maps a landscape of simple four-dimensional SCFTs generated from gauge theory with one adjoint and two fundamentals by exhaustively exploring relevant deformations, including gauge-singlet couplings. Using -maximization and the superconformal index as primary viability tests, the authors identify good fixed points—among them two enhanced Argyres–Douglas theories and and a minimal theory —as well as questionable fixed points with potential accidental symmetries and unphysical operators, notably a candidate minimal theory with very small and . The good theories exhibit emergent symmetry and operator decoupling, and their and values lie in a narrow band with , while the bad set hints at further structure (e.g., decoupled fermions) needed to resolve unitarity concerns. Overall, the paper provides a practical framework for enumerating and testing simple SCFTs via Lagrangian RG flows, highlighting near-minimal theories and raising questions about IR accidental symmetries and the true minimal fixed point in this landscape.

Abstract

We explore the space of renormalization group flows that originate from supersymmetric 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 . This set of theories includes two of the 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 that are smaller than any known superconformal theory -that need further investigation.

Paper Structure

This paper contains 9 sections, 17 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. A Landscape of Simple SCFTs
  3. ${\mathcal{T}}_0$ - minimal $c$, minimal $a$ with $U(1)$
  4. $H_0^*$ - minimal $a$
  5. $H_1^*$ - minimal $a$ with $SU(2)$
  6. ${\mathcal{T}}_\mu$ - next to minimal
  7. ${\mathcal{T}}_M$ -- a new minimal theory?
  8. Discussion
  9. APPENDIX: List of Candidate SCFTs

Figures (2)

  • 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 by the superpotential deformations. Note that the graph is not arranged vertically by decreasing $a$ central charge, because the deformations we consider involve coupling in the singlet fields.