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

Abstract

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 (An, Em) 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 $$ \mathcal{S} $$ S descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for $$ {D}_{h_G^{\vee }} $$ D h G ∨ (G) with $$ {h}_G^{\vee } $$ h G ∨ the dual Coxeter number of G; and the triviality of the 2-group structure in the (An, Em) theories.