Mirror Symmetry in Three Dimensions via Gauged Linear Quivers

Abstract

Starting from mirror pairs consisting only of linear (framed A-type) quivers, we demonstrate that a wide class of three-dimensional quiver gauge theories with N=4 supersymmetry and their mirror duals can be obtained by suitably gauging flavor symmetries. Infinite families of mirror pairs including various quivers of D and E-type and their affine extensions, star-shaped quivers, and quivers with symplectic gauge groups may be generated in this fashion. We present two different computational strategies to perform the aforementioned gauging procedure - one of them involves N=2* classical parameter space description, while the other one uses partition functions of the N=4 theories on S^3. The partition function, in particular, turns out to be an extremely efficient tool for implementing this gauging procedure as it readily generalizes to arbitrary size of the quiver and arbitrary rank of the gauge group at each node. For most examples of mirror pairs obtained via this procedure, we perform additional checks of mirror symmetry using the Hilbert series.

73 pages, many figures, typos corrected

References in corpus (11)

• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• S-duality in N=2 supersymmetric gauge theories
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• Supersymmetry enhancement by monopole operators
• Superconformal indices of three-dimensional theories related by mirror symmetry
• AGT on the S-duality Wall
• Tri-vertices and SU(2)'s
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n

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• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Fibrations and Hasse diagrams for 6d SCFTs
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• On Three-Dimensional Quiver Gauge Theories of Type B
• Good IR Duals of Bad Quiver Theories
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• A string theory realization of special unitary quivers in 3 dimensions
• Dualities and loops on squashed $S^3$