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

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.

56 pages and a number of figures. Version 2: references and comment added

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• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Magnetic quivers for rank 2 theories
• Fibrations and Hasse diagrams for 6d SCFTs
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Higgs, Coulomb, and Hall-Littlewood
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Discrete gauging and Hasse diagrams
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• FI-flows of 3d N=4 Theories
• Aspects of 4d supersymmetric dynamics and geometry