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)

Alexander Braverman; Hiraku Nakajima; Michael Finkelberg

arxiv: 1604.03625 · v5 · pith:WHWYEFE5new · submitted 2016-04-13 · 🧮 math.RT · hep-th· math-ph· math.AG· math.DG· math.MP

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)

Alexander Braverman , Michael Finkelberg , Hiraku Nakajima This is my paper

classification 🧮 math.RT hep-thmath-phmath.AGmath.DGmath.MP

keywords coulombaffinealexbranchescaseframedgaugegrassmannian

0 comments

read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type
hep-th 2025-03 unverdicted novelty 7.0

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.
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
math.AG 2020-01 unverdicted novelty 7.0

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.
From Quivers to Geometry: 5d Conformal Matter
hep-th 2026-05 unverdicted novelty 6.0

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.
Quiver Yangians as Coulomb branch algebras
hep-th 2025-02 unverdicted novelty 6.0

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.
A mathematical definition of Coulomb branches of supersymmetric gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras
math.RT 2022-01 unverdicted novelty 2.0

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.