Higher Form Symmetries of Argyres-Douglas Theories

TL;DR

This paper determines the structure of 1-form symmetries in a broad class of 4d $ abla=2$ theories, including Argyres-Douglas models, using geometric engineering and BPS quivers, providing new insights into their symmetry properties.

Contribution

It introduces a method to compute 1-form symmetries for theories without known gauge descriptions via IIB string theory and BPS quivers, extending understanding of these symmetries in complex models.

Findings

1-form symmetries are derived from RR flux analysis at infinity.

Results match with proposed $ abla=1$ gauge theory descriptions where available.

Method applies to a large class of theories including Argyres-Douglas models.

Abstract

We determine the structure of 1-form symmetries for all 4d $\mathcal{N} = 2$ 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 $(\mathfrak{g}, \mathfrak{g}')$ Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where $\mathcal{N} = 1$ gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such $\mathcal{N} = 1$ Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.