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Consider the $3$-dimensional N=4 supersymmetric gauge theory associated with a compact Lie group Gc and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler manifold with an SU(2)-action, possibly with singularities. We give a mathematical definition of the Coulomb branch as an affine algebraic variety with C^×-action when M is of a form N⊕ N^*, as the second step of the proposal given in arXiv:1503.03676.
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Braverman et al. (2018) studied this question.
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