3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
Emanuele Beratto, Simone Giacomelli, Noppadol Mekareeya, Matteo Sacchi
TL;DR
The paper develops a 3d mirror construction for the $S^1$ reduction of twisted $A_{2N}$ class~S theories, describing an almost star-shaped quiver with a central $USp(2N)$ node and mixed gauge factors that encapsulates the mirrors. It provides a concrete framework using $T_{m{\rho}}(SU(2N{+}1))$ and $T^{\bm{\sigma}}_{\bm{\rho}}(USp'(2N))$ building blocks, and validates the proposal via detailed Hilbert-series checks that match the 4d Higgs branches with the 3d Coulomb branches, including mass and FI deformations that reproduce known IR theories. The work also extends to twisted $A_2$ theories with four punctures and general $N$, uncovering dual pairs and symmetry enhancements, and it predicts new RG flows such as a SUSY enhancement to $SO(4)$ $\mathcal{N}=4$ SYM in a mass deformation of the $\widetilde{T}_3$ theory. Overall, the results provide a coherent 3d mirror dictionary for twisted $A_{2N}$ theories, with multiple dual descriptions and nontrivial checks against Beem–Peelaers 4d constructions. This framework enhances understanding of how higher-dimensional SCFT data surface in 3d moduli spaces and suggests avenues for non-simply-laced quiver realizations.
Abstract
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$ in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.