Towards a mathematical definition of Coulomb branches of $3$-dimensional   $\mathcal N=4$ gauge theories, II
  Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler manifold with an $\mathrm{SU}(2)$-action, possibly with singularities. We give a mathematical definition of the Coulomb branch as an affine algebraic variety with $\mathbb C^\times$-action when $\mathbf M$ is of a form $\mathbf N\oplus\mathbf N^*$, as the second step of the proposal given in arXiv:1503.03676. 
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima
math.RT hep-th math-ph math.AG math.DG math.MP