Lagrangians for generalized Argyres-Douglas theories
Sergio Benvenuti, Simone Giacomelli
TL;DR
The paper provides Lagrangian UV completions for generalized Argyres-Douglas theories by deploying 3d mirror symmetry and a sequential confinement mechanism to flow to Abelian ${\mathcal{N}}=4$ complete-graph quivers. It shows how these 3d flows determine 4d ${\mathcal{N}}=1$ Lagrangians that, upon appropriate nilpotent deformations, realize AD fixed points such as the $A_k$ and $D_{2N}$ families, with explicit mappings between chiral rings and Coulomb/Higgs branches. The authors verify consistency through concrete examples (e.g., the Abelianization to ${\mathcal{N}}=4$ SQED with 3 flavors for $(A_1,D_4)$) and by matching central charges, thereby providing a systematic route to Lagrangian descriptions of AD theories. The framework broadens the landscape of Lagrangian UV completions for strongly coupled ${\mathcal{N}}=2$ SCFTs and paves the way for index and moduli-space analyses via their 3d mirrors and dualities.
Abstract
We continue the study of Lagrangian descriptions of $\mathcal{N}=2$ Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional $\mathcal{N}=1$ quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the $(A_k,A_{kN+N-1})$ models. We study in detail how the $\mathcal{N}=1$ chiral rings map to the Coulomb and Higgs Branches of the $\mathcal{N}=2$ CFT's. The three dimensional mirror RG flows are shown to land on the $\mathcal{N}=4$ complete graph quivers. We also compactify to three dimensions the gauge theory dual to $(A_1,D_4)$, and find the expected Abelianization duality with $\mathcal{N}=4$ SQED with $3$ flavors.