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This is a supplement to [arXiv:1503.03676], where an approach towards amathematically rigorous definition of the Coulomb branch of a $3$-dimensional$\mathcal N=4$ SUSY gauge theory was proposed. We ask questions on theirexpected properties, especially in relation to the corresponding Higgs branch,partly motivated by the interpretation of the level rank duality in terms ofquiver varieties [arXiv:0809.2605] and the symplectic duality[arXiv:1407.0964]. We study questions in a few examples.

Questions on provisional Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories