Coulomb branches of 3d $N=4$ gauge theories and the affine Grassmannian

Abstract: We propose a mathematically rigorous definition of Coulomb branch of a 3d $N=4$ SUSY gauge theory, as an affine algebraic variety, based on the homology group of a variant of the affine Grassmannian. In particular, coordinate rings of various hyper-Kaehler manifolds, such as instanton moduli spaces on ALE spaces, nilpotent orbits, etc, are conjecturally given by such a construction.

nakajima@kurims.kyoto-u.ac.jp