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Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II (1601.03586v8)
Published 14 Jan 2016 in math.RT, hep-th, math-ph, math.AG, math.DG, and math.MP
Abstract: 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.