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)

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.

56 pages; v2. A reference added; v3. 66 pages. A new subsection `Towards geometric Satake correspondence for Kac-Moody Lie algebras' added. The definition of the shifted Yangian corrected; v4. \circ, \bullet on characters are changed; v5. Remarks 3.7, 3.8, 3.19 are corrected

References in corpus (6)

• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)
• Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
• Lectures on perverse sheaves on instanton moduli spaces
• Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groups
• Integrable crystals and restriction to Levi via generalized slices in the affine Grassmannian

Cited by in corpus (29)

• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras
• Coulomb branches of quiver gauge theories with symmetrizers
• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)
• Koszul duality between Higgs and Coulomb categories $\mathcal{O}$
• Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties
• Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices
• Quantum q-Langlands Correspondence
• Generators for Coulomb branches of quiver gauge theories
• Line bundles over Coulomb branches
• Ring Relations and Mirror Map from Branes
• Gelfand-Tsetlin modules in the Coulomb context
• Towards geometric Satake correspondence for Kac-Moody algebras -- Cherkis bow varieties and affine Lie algebras of type $A$
• Coherent sheaves and quantum Coulomb branches I: tilting bundles from integrable systems
• Little String Defects and Bala-Carter Theory
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• A Family of ${\mathrm{GL}}_r$ Multiplicative Higgs Bundles on Rational Base
• Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
• Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type $A$
• Some Open Questions in Quiver Gauge Theory
• Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products
• Coulomb branch of a multiloop quiver gauge theory
• Instantons and Bows for the Classical Groups
• 't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories