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

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 $(G,G^{\prime })$ 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 $D_{h_G^{\vee }}(G)$ with $h_G^{\vee }$ the dual Coxeter number of $G$; and the triviality of the 2-group structure in the $(A_n,E_m)$ theories.

arXiv commentv2: add references, JHEP accepted; v1: 35 pages + 3 appendices

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• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Higgs, Coulomb, and Hall-Littlewood
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• A tale of 2-groups: D${}_p$(USp(2N)) theories