Higher form symmetries of Argyres-Douglas theories

Abstract

AbstractWe determine the structure of 1-form symmetries for all 4d $$ \mathcal{N} $$ N = 2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the ($$ \mathfrak{g},{\mathfrak{g}}^{\prime } $$ g , g ′ ) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where $$ \mathcal{N} $$ N = 1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such $$ \mathcal{N} $$ N = 1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.