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

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.Comment: v2: add references, JHEP accepted; v1: 35 pages + 3 appendice