Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories

TL;DR

The paper provides a comprehensive map of conformal manifolds for two infinite AD families, $D^b_p(\mathrm{SO}(2N))$ and $(A_m,D_n)$, via twisted puncture class ${\cal S}$ constructions and IIB CY geometries. It delivers systematic 3d magnetic-quiver mirrors for the relevant theories, including reductions and discrete gauging subtleties, and analyzes RG flows with supersymmetry enhancement (MS flows) to constrain the mirrors. A unified framework is presented for the conformal-manifold dimensions across gcd cases, with explicit weakly coupled cusps described by orthosymplectic and unitary gaugings and partially closed punctures, as well as numerous detailed examples and non-Higgsable SCFT identifications. The work also develops and tests a Flip-Flip duality extension for $T[\mathrm{SO}(2N)]$ to illuminate MS-flow effects on 3d mirrors, and it highlights the role of defect groups and 1-form symmetries in potential discrete gaugings. Overall, the results deepen the holographic/class-${\cal S}$ understanding of AD theories and provide concrete 3d descriptions, enabling cross-checks via CB/HB Hilbert series and central charges.

Abstract

Argyres-Douglas theories constitute an important class of superconformal field theories in $4$d. The main focus of this paper is on two infinite families of such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze in depth their conformal manifolds. In doing so we encounter several theories of class $\mathcal{S}$ of twisted $A_{\text{odd}}$, twisted $A_{\text{even}}$ and twisted $D$ types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include $D_p(G)$ theories, with $G$ non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the $3$d mirror theories, also known as the magnetic quivers, for the $D^b_p(\mathrm{SO}(2N))$ theories, with $p \geq b$, and the $(A_m, D_n)$ theories, with arbitrary $m$ and $n$. We also discuss the $3$d reduction and mirror theories of certain $D^b_p(\mathrm{SO}(2N))$ theories, with $p < b$, where the former arises from gauging topological symmetries of some $T^σ_ρ[\mathrm{SO}(2M)]$ theories that are not manifest in the Lagrangian description of the latter.