Generators for Coulomb branches of quiver gauge theories

Abstract

We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation parameter is set to $\hslash =1$. In finite ADE type, this extends to a surjection over $\mathbb{C}[\hslash ]$. We also show that these algebras are generated by the dressed minuscule monopole operators, for an arbitrary quiver (this is similar to the proof of Theorem 4.29 in arXiv:1811.12137). Finally, we describe how the KLR Yangian algebra from arXiv:1806.07519 is related to Webster's extended BFN category. This paper provides proofs for two results which were announced in arXiv:1806.07519.

arXiv comment22 pages, comments welcome; v2. 27 pages, new proof of part (b) of Theorem A given in Section 3.4.2, connection with OGZ algebras added in Section 3.5, other minor changes throughout

References in corpus (17)

• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Yangians and quantizations of slices in the affine Grassmannian
• 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)
• On a class of representations of the Yangian and moduli space of monopoles
• An introduction to affine Grassmannians and the geometric Satake equivalence
• Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras
• 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 $\mathcal{O}$
• Principal Galois orders and Gelfand-Zeitlin modules
• Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra
• Gelfand-Tsetlin modules in the Coulomb context
• Coulomb Branches of Star-Shaped Quivers
• Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories
• Steenrod Operators, the Coulomb Branch and the Frobenius Twist, I
• Coulomb branch of a multiloop quiver gauge theory

Cited by in corpus (7)

• Coulomb branches of quiver gauge theories with symmetrizers
• Twisted M2 brane holography and sphere correlation functions
• BFN Springer Theory
• Gelfand-Tsetlin modules in the Coulomb context
• Branes, Quivers, and the Affine Grassmannian
• $K$-theoretic Coulomb branches of quiver gauge theories and cluster varieties
• Coulomb branch of a multiloop quiver gauge theory