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Mirror Symmetry in Three Dimensional Gauge Theories
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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.
Forward citations
Cited by 24 Pith papers
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3d $\mathcal N=4$ rank-zero mirror symmetry, TQFT interfaces, and Zagier duality of Nahm sums
Zagier duality between the (E8,T1) and (T1,E8) Nahm systems is realized as 3d N=4 rank-zero mirror symmetry of two U(1)^8 Chern-Simons matter theories, with the duality interface generating the level-one E8 character.
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New symplectic singularities from $SU(2)$ gauge theories
An SU(2) gauge theory with one Sym^k half-hypermultiplet and N fundamental half-hypermultiplets yields isolated symplectic singularities for k=1,3,5,7, with k=5,7 giving the new families hSO(N) and iSO(N).
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Algorithmic Dualization of Unitary Circular Quivers
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Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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Vertex Superalgebras for Hypertoric Varieties and 3d Abelian Gauge Theories
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Planar Abelian Duals of Chern-Simons QCD
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Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type
Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
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Classification of Minimal Abelian Coulomb Branches
Abelian 3d N=4 quivers with isolated Coulomb branch singularities are exactly stable chains and well-defined cycles, with geometries given by U(1) or finite cyclic quotients.
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Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
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Instantons from Blow-up
The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.
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Chiralization of Quiver Varieties
Constructs two vertex superalgebras chiralizing extended quiver varieties and establishes a map between them with vanishing and injectivity results under technical assumptions.
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A Tale of Two Orbits: Non-Simply Laced Mirror
A 3D N=4 gauge theory is built via U(1) gauging whose Higgs branch matches a known symplectic singularity, with a proposed non-simply laced magnetic quiver mirror validated through standard 3D mirror symmetry tests.
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Bootstrapping mirror pairs: The beginning of the end
A growth-and-fusion algorithm completes a quartet of quiver operations that bootstrap 3d mirror pairs, demonstrated on a new family of circular 'sunshine' quivers.
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Hilbert Series and Superconformal Indices of the Improved Bifundamentals
The vacuum moduli spaces of the improved bifundamental SCFTs are claimed to be single-branch irreducible varieties, with Hilbert series extracted from superconformal index limits.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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Time-reversal invariant TQFTs from self-mirror symmetric SCFTs
Self-mirror symmetric Abelian 3d N=4 SCFTs deform to time-reversal invariant Abelian Chern-Simons theories, with a charge-matrix constraint Q Omega Q^T = 0 governing the correspondence.
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3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching
Universal mass deformations of 3d N=4 Abelian gauge theories flow to Abelian spin Chern-Simons TQFTs, with mirror symmetry descending to proven level-rank dualities and 't Hooft anomalies matched via vison fractionalization.
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Non-invertible twisted compactification of class $\mathcal S$ theory and $(B,B,B)$ branes
Non-invertible twisted compactification of class S theories on S^1 produces 3d N=4 sigma models whose target spaces are fixed-point sets of mapping class group actions on Hitchin moduli space, i.e. (B,B,B) branes.
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Mirror symmetry for 4d $A_1$ class-$\mathcal{S}$ theories: modularity, defects and Coulomb branch
A conjectured 4d mirror symmetry for A1 class-S theories matches simple modules of the Higgs-branch VOA to fixed manifolds of the Hitchin Coulomb branch, with conformal weights and modular Jordan types fixed by moment...
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A Bound on 3d Mirror Pairs
New 3d mirror pairs are proposed for ABCD-type quivers with mixed U/SU nodes, and it is conjectured that unitary quivers containing exceptional affine Dynkin subquivers have no Lagrangian quiver mirror.
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An exceptionally simple family of Orthosymplectic 3d $\mathcal{N}=4$ rank-0 SCFTs
A new family of 3d N=4 orthosymplectic quiver theories has trivial Higgs branches and non-trivial Coulomb branches; the smallest full moduli space is two copies of the one-F4 instanton moduli space.
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On classification of rank two theories with eight supercharges Part III: Seiberg-Witten geometry
The abstract claims rank-two Seiberg-Witten geometries can be systematized via one-parameter curve families y^2 = f(x,t), with f fixed by singular fibers at t = infinity.
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A Crash Course in Supersymmetric Field Theory Across Dimensions
Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.
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