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Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories

Federico Carta, Simone Giacomelli, Noppadol Mekareeya, Alessandro Mininno

TL;DR

This work investigates 1-form symmetries in four-dimensional Argyres-Douglas theories and their consequences under Higgs-branch flows and 3d reduction, showing that nontrivial 1-form symmetry is captured by non-Higgsable sectors and leads to free sectors upon reduction to 3d. Building on this, the authors systematically construct 3d mirrors for the (A_n,E_m) AD theories, leveraging Flip-Flip duality for T[G], MS flows, and D_p(G) structures, and they extend the framework to exceptional groups with explicit root-data-based quiver constructions. The paper also derives 3d mirrors for (D_n,E_m) theories, including detailed 4-mass and 0-mass cases, and discusses the role of crepant divisors in shaping the Higgs branches and mirror gauge content, providing partial checks via mass deformations and gauging of baryonic/topological symmetries. Overall, the results yield new, checkable dual descriptions across the ADE families, reveal universality patterns for certain mirrors, and argue against the presence of 2-group structure in these AD theories, with implications for class-S realizations and exceptional affine Dynkin quivers.

Abstract

Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the $(G,G')$ type, we find that the 1-form symmetries are invariant under the Higgs branch flow, and that they are captured by the non-Higgsable sector at a generic point on the Higgs branch of the AD theory in question. As a consequence, dimensional reduction of an AD theory with a non-trivial 1-form symmetry to 3d leads to a free sector. We utilize these observations, along with other results, to propose systematically the mirror theories for the AD theories of the $(A_n, E_m)$ type. As a by-product of these findings, we discover many important results: the Flip-Flip duality for all $T[G]$ theories with simply-laced group $G$, including the exceptional ones; the class $\mathcal{S}$ descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for $D_{h^\vee_G}(G)$ with $h^\vee_G$ the dual Coxeter number of $G$; and the triviality of the 2-group structure in the $(A_n, E_m)$ theories.

Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories

TL;DR

This work investigates 1-form symmetries in four-dimensional Argyres-Douglas theories and their consequences under Higgs-branch flows and 3d reduction, showing that nontrivial 1-form symmetry is captured by non-Higgsable sectors and leads to free sectors upon reduction to 3d. Building on this, the authors systematically construct 3d mirrors for the (A_n,E_m) AD theories, leveraging Flip-Flip duality for T[G], MS flows, and D_p(G) structures, and they extend the framework to exceptional groups with explicit root-data-based quiver constructions. The paper also derives 3d mirrors for (D_n,E_m) theories, including detailed 4-mass and 0-mass cases, and discusses the role of crepant divisors in shaping the Higgs branches and mirror gauge content, providing partial checks via mass deformations and gauging of baryonic/topological symmetries. Overall, the results yield new, checkable dual descriptions across the ADE families, reveal universality patterns for certain mirrors, and argue against the presence of 2-group structure in these AD theories, with implications for class-S realizations and exceptional affine Dynkin quivers.

Abstract

Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the type, we find that the 1-form symmetries are invariant under the Higgs branch flow, and that they are captured by the non-Higgsable sector at a generic point on the Higgs branch of the AD theory in question. As a consequence, dimensional reduction of an AD theory with a non-trivial 1-form symmetry to 3d leads to a free sector. We utilize these observations, along with other results, to propose systematically the mirror theories for the AD theories of the type. As a by-product of these findings, we discover many important results: the Flip-Flip duality for all theories with simply-laced group , including the exceptional ones; the class descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for with the dual Coxeter number of ; and the triviality of the 2-group structure in the theories.
Paper Structure (28 sections, 62 equations, 1 table)

This paper contains 28 sections, 62 equations, 1 table.

Table of Contents

  1. Introduction
  2. 1-form symmetries
  3. Realization in a weakly-gauged description
  4. Maruyoshi-Song procedure
  5. Flip-Flip duality for $T[G]$
  6. $D_p(G)$ theories and special unitary quivers with exceptional shape
  7. The mirror dual of $D_{h^{\vee}_G}(G)$ and $(A_{\mathfrak{n} h^{\vee}_G-1},G)$
  8. $(A_n,E_m)$ theories
  9. 3d mirror theories for $(A_n,E_6)$
  10. 6 mass parameters
  11. 2 mass parameters
  12. 0 mass parameter
  13. 3d mirror theories for $(A_n,E_7)$
  14. 7 mass parameters
  15. 1 mass parameter
  16. ...and 13 more sections