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.

22 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 (2)

• Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories
• Steenrod Operators, the Coulomb Branch and the Frobenius Twist, I