3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$

TL;DR

This paper proposes a new quiver description for the mirror theories of circle reductions of twisted $A_{2N}$ class $ extsf{S}$ theories, enabling detailed analysis of their moduli spaces and revealing a novel supersymmetry enhancement flow.

Contribution

It introduces a novel quiver framework involving diverse gauge groups for these mirror theories, with detailed moduli space analysis and evidence for supersymmetry enhancement.

Findings

Coulomb and Higgs branch Hilbert series match, confirming the proposal.

Deformations lead to expected theories, supporting the quiver description.

Discovery of a new supersymmetry enhancement RG flow.

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.