Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories

We propose a conjectural construction of various slices for double affine Grassmannians as Coulomb branches of 3-dimensional N=4 supersymmetric affine quiver gauge theories. It generalizes the known construction for the usual affine Grassmannian, and makes sense for arbitrary symmetric Kac-Moody algebras.