Mirror Symmetry in Three Dimensional Gauge Theories

Abstract

We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group. In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.

13 pages, harvmac

References in corpus (3)

• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Gauge Dynamics And Compactification To Three Dimensions
• The Moduli Space of Many BPS Monopoles for Arbitrary Gauge Groups

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• Discrete Torsion in Singular G_2-Manifolds and Real LG
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Deformations of the moduli space and superpotential flows in 3D SUSY QCD
• Solving Four Dimensional Field Theories with the Dirichlet Fivebrane
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• Dualities and loops on squashed $S^3$
• Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications
• Instantons and Bows for the Classical Groups
• A plethora of K3 metrics
• Branes and Fundamental Groups
• Dualities in integrable systems and N=2 theories
• Anomalous N=2 superconformal Ward identities
• A survey of recent developments in GLSMs
• Monopole operators and symmetry enhancement in ABJM theory revisited
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• Domain Wall and Three Dimensional Duality
• Coulomb Branch for A-type Balanced Quivers in 3d $\mathcal{N}=4$ gauge theories
• $\mathcal{N}=2$ ${\text{CFT}}_3\text{’s}$ from $\mathcal{N}=4$ gauged supergravity
• The braneology of 3D dualities
• Charges of Monopole Operators in $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories
• Sequential deconfinement and self-dualities in $4d$ $\mathcal{N}=1$ gauge theories
• New AdS${}_3$/CFT${}_2$ pairs in massive IIA with $(0,4)$ and $(4,4)$ supersymmetries
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas
• Superconformal D-branes and moduli spaces
• A Note on Singular Black Holes
• Virtual Coulomb branch and vertex functions
• Stable envelopes for slices of the affine Grassmannian
• Single-flavor Abelian mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$
• Non-perturbative N=1 strings from geometric singularities
• Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories
• FI-flows of 3d N=4 Theories
• Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence
• Localized Kaluza-Klein 6-brane