Abelianization and Sequential Confinement in $2+1$ dimensions

TL;DR

This work addresses how to obtain Lagrangian descriptions for the $A_{2N-1}$ Argyres-Douglas theories and their $3d$ mirrors by refining the Maruyoshi–Song construction. The authors introduce gauge-singlet fields to decouple unitarity-violating operators and apply chiral-ring stability to remove a superpotential term, yielding ${\mathcal{T}}'_{4d,UV}$ and ${\mathcal{T}}'_{4d,IR}$ whose $3d$ reductions can be consistently analyzed. In three dimensions, the adjoint SQCD abelianizes to a $U(1)^{N-1}$ linear quiver in the IR, and via monopole dualities the mirror flow lands on $\mathcal{N}=4$ SQED with $N$ flavors, aligning with established $3d$ mirrors of AD theories. These results provide a concrete physical derivation of the 3d mirror descriptions for the AD class and clarify how operator decoupling and stability constraints shape the IR dynamics across dimensions.

Abstract

We consider the lagrangian description of Argyres-Douglas theories of type $A_{2N-1}$, which is a $SU(N)$ gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD "abelianizes": in the infrared it is equivalent to a $\mathcal{N}=4$ linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to "sequentially confine" quivers tails with balanced nodes, we show that the mirror RG flow lands on $\mathcal{N}=4$ SQED with $N$ flavors. These results provide a physical derivation of previous proposals for the three dimensional mirror of AD theories.