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.
Coulomb branches of $3d$ $\mathcal N=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
8 Pith papers cite this work, alongside 113 external citations. Polarity classification is still indexing.
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abstract
This is a companion paper of arXiv:1601.03586. We study Coulomb branches of unframed and framed quiver gauge theories of type $ADE$. In the unframed case they are isomorphic to the moduli space of based rational maps from ${\mathbb C}P^1$ to the flag variety. In the framed case they are slices in the affine Grassmannian and their generalization. In the appendix, written jointly with Joel Kamnitzer, Ryosuke Kodera, Ben Webster, and Alex Weekes, we identify the quantized Coulomb branch with the truncated shifted Yangian.
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Proves formula for Euler numbers of Hilb^n(C²/Γ) by establishing that quantum dimensions of standard modules of associated quantum affine algebras are 1 at a specific root of unity, including for E7 and E8 cases.
Derives conjugation formulas for unitriangular R-matrices of quantum affine algebras and Yangians using T-series of Frenkel-Hernandez and prior Theta series.
Constructs two vertex superalgebras chiralizing extended quiver varieties and establishes a map between them with vanishing and injectivity results under technical assumptions.
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.
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.
All 5d balanced (ADE-shaped) SU quivers with no Chern-Simons level have UV completions as 5d conformal matter SCFTs realized by explicit local Calabi-Yau threefolds in M-theory.
Introductory article presenting a mathematical definition of Coulomb branches of 3d N=4 SUSY gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras based on those branches.
citing papers explorer
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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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Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
Proves formula for Euler numbers of Hilb^n(C²/Γ) by establishing that quantum dimensions of standard modules of associated quantum affine algebras are 1 at a specific root of unity, including for E7 and E8 cases.
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Unitriangular R-matrices of quantum affine algebras and Yangians via Theta series
Derives conjugation formulas for unitriangular R-matrices of quantum affine algebras and Yangians using T-series of Frenkel-Hernandez and prior Theta series.
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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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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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From Quivers to Geometry: 5d Conformal Matter
All 5d balanced (ADE-shaped) SU quivers with no Chern-Simons level have UV completions as 5d conformal matter SCFTs realized by explicit local Calabi-Yau threefolds in M-theory.
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A mathematical definition of Coulomb branches of supersymmetric gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras
Introductory article presenting a mathematical definition of Coulomb branches of 3d N=4 SUSY gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras based on those branches.