N=1 Lagrangians for generalized Argyres-Douglas theories

TL;DR

The paper constructs UV ${\cal N}=1$ Lagrangian gauge theories by implementing nilpotent deformations of ${\cal N}=2$ quivers, showing that they flow in the IR to generalized Argyres-Douglas theories of several types. For SU-based quivers, flows to $(A_{m-1}, A_{Nm-1})$ and $(I_{m, mk}, S)$ are demonstrated; for SO/Sp quivers, flows to $(A_{2m-1}, D_{2Nm+1})$, $(A_{2m}, D_{m(N-2)+N/2})$, and $D_{m(2N+2)}^{m(2N+2)}[m]$ are shown. In each case, theIR central charges and Coulomb branch spectra match the corresponding AD data after decoupling free fields, providing UV Lagrangian realizations of these non-Lagrangian fixed points and supporting SUSY enhancement to ${\cal N}=2$ in principal embedding scenarios. The work suggests broad avenues for computing indices, exploring dualities, and reducing to lower dimensions to further illuminate the structure of AD theories.

Abstract

We find $\mathcal{N}=1$ Lagrangian gauge theories that flow to generalized Argyres-Douglas theories with $\mathcal{N}=2$ supersymmetry. We find that certain SU quiver gauge theories flow to generalized Argyres-Douglas theories of type $(A_{k-1}, A_{mk-1})$ and $(I_{m, k m}, S)$. We also find quiver gauge theories of SO/Sp gauge groups flowing to the $(A_{2m-1}, D_{2mk+1})$, $(A_{2m}, D_{2m(k-1)+k})$ and $D_{m(2k+2)}^{m(2k+2)}[m]$ theories.