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Generalized symmetry constraints on deformed 4d (S)CFTs

Monica Jinwoo Kang, Craig Lawrie, Ki-Hong Lee, Jaewon Song

TL;DR

The paper develops a systematic framework to constrain IR physics of 4d gauge theories by exploiting generalized symmetries, focusing on one-form and zero-form anomalies. It classifies all simple, simply-connected 4d $\mathcal{N}=1$ theories with nontrivial one-form symmetry that flow to SCFTs, identifies remnant discrete axial symmetries via ABJ anomalies, and analyzes mixed zero-form/one-form anomalies that must be matched along RG flows. The work further explores relevant deformations that preserve parts of these anomalies, constraining whether RG flows can reach trivially gapped phases or require symmetry breaking or topological sectors, with explicit treatment of non-Lagrangian Argyres–Douglas matter and new dualities (e.g., diagonal gauging of $\mathcal{D}_3(SU(N))$ vs. two-adjoint SQCD). It also extends the analysis to a non-supersymmetric setting and highlights Banks–Zaks-type fixed points as potential IR endpoints. Overall, the results provide a robust anomaly-based toolkit to diagnose IR phases and dualities in deformed 4d gauge theories with generalized global symmetries, including non-Lagrangian sectors and intricate global structures.

Abstract

We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two $\mathcal{D}_3(SU(N))$ theories and $SU(N)$ gauge theory with two adjoints. We also repeat our analysis for a host of non-supersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs.

Generalized symmetry constraints on deformed 4d (S)CFTs

TL;DR

The paper develops a systematic framework to constrain IR physics of 4d gauge theories by exploiting generalized symmetries, focusing on one-form and zero-form anomalies. It classifies all simple, simply-connected 4d theories with nontrivial one-form symmetry that flow to SCFTs, identifies remnant discrete axial symmetries via ABJ anomalies, and analyzes mixed zero-form/one-form anomalies that must be matched along RG flows. The work further explores relevant deformations that preserve parts of these anomalies, constraining whether RG flows can reach trivially gapped phases or require symmetry breaking or topological sectors, with explicit treatment of non-Lagrangian Argyres–Douglas matter and new dualities (e.g., diagonal gauging of vs. two-adjoint SQCD). It also extends the analysis to a non-supersymmetric setting and highlights Banks–Zaks-type fixed points as potential IR endpoints. Overall, the results provide a robust anomaly-based toolkit to diagnose IR phases and dualities in deformed 4d gauge theories with generalized global symmetries, including non-Lagrangian sectors and intricate global structures.

Abstract

We explore the consequence of generalized symmetries in four-dimensional superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two theories and gauge theory with two adjoints. We also repeat our analysis for a host of non-supersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs.
Paper Structure (29 sections, 308 equations, 9 tables)

This paper contains 29 sections, 308 equations, 9 tables.

Table of Contents

  1. Introduction
  2. N=1 gauge theories with one-form symmetry
  3. One-form symmetry
  4. Conformal window
  5. N=1 theories with zero-form/one-form anomaly
  6. Global zero-form symmetry and anomalies
  7. The global zero-form symmetry
  8. $\mathbf{U(1)'_i}$ -- $\mathbf{U(1)'_j}$:
  9. $\mathbf{U(1)'_i}$ -- $\mathbf{U(1)_R}$:
  10. $\mathbf{U(1)_i'}$ -- $\mathbf{\mathbb{Z}^A}$:
  11. $\mathbf{U(1)_R}$ -- $\mathbf{\mathbb{Z}^A}$:
  12. $\mathbf{(U(1)_i'\times \mathbb{Z}^A)-Z(G)}$:
  13. The global structure:
  14. Anomalies
  15. Relevant deformations
  16. ...and 14 more sections