Simplifying the Type $A$ Argyres-Douglas Landscape

TL;DR

This work shows that the landscape of type A Argyres–Douglas theories can be dramatically simplified by expressing many theories with irregular Hitchin data as gaugings of a small set of coprime Type I building blocks, supplemented by free hypermultiplets. The authors develop a unified framework linking irregular Hitchin data, 3d reductions and mirrors, central charges, and vertex operator algebras, using two main equivalences in the coprime case and a generalized gauging construction for non-coprime cases. They provide concrete evidence via Coulomb branch spectra, 3d reductions, and VOA considerations, and they derive explicit rules for counting free hypermultiplets that preserve conformality and flavor symmetry. The results yield an economical, diagrammatic understanding of the AD Type A landscape, with clear pathways to extendings to other types and to holographic duals.

Abstract

A well-established organisational principle for Argyres--Douglas-type $\mathcal{N}=2$ superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on $\mathbb{CP}^1$. The dictionary between Hitchin system data and various features of the corresponding SCFT has been studied extensively, but the overall structure of the resulting space of SCFTs still appears quite complicated. In this work, we systematically delineate a variety of simplifications that arise within this class of constructions due to several large classes of isomorphisms between SCFTs associated with inequivalent Hitchin system data (and their exactly marginal gaugings). We restrict to the most studied class of theories, namely the type $A$ theories without outer automorphism twists.

Figures (5)

• Figure 1: The 3d $\mathcal{N}=4$ quiver gauge theory that is mirror dual to the circle reduction of the $D_{p}^{b}\left(\mathfrak{sl}_{N},[1^N]\right)$ Argyres--Douglas theory for $p>b$. The number of $\mathfrak{u}(1)$ gauge nodes in the complete graph is in general $m$, but for simplicity in the drawing we depict the case of $m=3$. The numbers labelling certain edges denote the multiplicity of the corresponding hypermultiplet, where the absence of an explicit label implies unit multiplicity.
• Figure 2: The 3d $\mathcal{N}=4$ quiver theory that is mirror dual to the circle reduction of the type I Argyres--Douglas $D_{p}\left(\mathfrak{sl}_{N},[1^N]\right)$ theory for $p>N$. The number of $\mathfrak{u}(1)$ gauge nodes in the complete graph is in general $m$, but for simplicity in the drawing we depict the case of $m=3$.
• Figure 3: The 3d $\mathcal{N}=4$ quiver theory that is mirror dual to the circle reduction of the $D_{p}^{b}\left(\mathfrak{sl}_{N},[1^N]\right)$ Argyres--Douglas theory for $p<b$. The number of $\mathfrak{u}(1)$ gauge nodes in the complete graph is in general $m$, but for simplicity in the drawing we depict the case of $m=3$.
• Figure 4: The 3d $\mathcal{N}=4$ quiver theory that is mirror dual to the circle reduction of the $D_{p}\left(\mathfrak{sl}_{N},[1^N]\right)$ Argyres--Douglas theory for $p<N$. The number of $\mathfrak{u}(1)$ gauge nodes in the complete graph is in general $m$, but for simplicity in the drawing we depict the case of $m=3$.
• Figure 5: Schematic representation of the various RG flows triggered by nilpotent vevs that relate the theories in \ref{['eq:GentypeIiso']} for different choices of the partition $[Y]$.