Lagrangians for generalized Argyres-Douglas theories

TL;DR

This paper advances the understanding of Lagrangian descriptions for a class of four-dimensional $ abla$2$ Argyres-Douglas theories, proposing new Lagrangians, analyzing their RG flows, and exploring their three-dimensional mirror dualities.

Contribution

It introduces Lagrangian models for generalized Argyres-Douglas theories and studies their RG flows and mirror dualities, extending previous frameworks.

Findings

Proposed Lagrangians for all Argyres-Douglas models with Abelian 3D mirrors.

Analyzed RG flows to $ abla$4$ complete graph quivers.

Confirmed Abelianization duality with $ abla$4$ SQED with 3 flavors.

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.