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The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bareand dressed BPS monopole operators. We utilise the conformal dimension todefine a fan which, upon intersection with the weight lattice of a GNO-dualgroup, gives rise to a collection of semi-groups. It turns out that the uniqueHilbert bases of these semi-groups are a sufficient, finite set of monopoleoperators which generate the entire chiral ring. Moreover, the knowledge of theproperties of the minimal generators is enough to compute the Hilbert seriesexplicitly. The techniques of this paper allow an efficient evaluation of theHilbert series for general rank gauge groups. As an application, we providevarious examples for all rank two gauge groups to demonstrate the novelinterpretation.

Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories