Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 1

Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian

Pages: 75 – 166



Alexander Braverman (Department of Mathematics, University of Toronto, Ontario, Canada; and the Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada)

Michael Finkelberg (Department of Mathematics, National Research University Higher School of Economics, Moscow, Russia; Skolkovo Institute of Science and Technology, Moscow, Russia; and Institute for Information Transmission Problems, Moscow, Russia)

Hiraku Nakajima (Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan; and Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba, Japan)


This is a companion paper of [Part II].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 $\mathbb{P}^1$ 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, BenWebster, and AlexWeekes, we identify the quantized Coulomb branch with the truncated shifted Yangian.

With two appendices by Alexander Braverman Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes.

Published 27 September 2019